Course information: Advanced Dynamics & Computation - ME331A Advanced Dynamics & Simulation - ME331B Instructor Office location Software Web sites Course elements
Course material Distributed in class
Paul Mitiguy 650-346-9595 113 Peterson (Building 550 - D.School) R R MATLAB , MotionGenesisTM, . . . (MotionGenesisTM is a MATLAB connections partner) www.stanford.edu/class/me331a www.MotionGenesis.com Lecture, computation/office hours, colleagues, homework, MIPSI, book. Advanced Dynamics & Motion Simulation $125 For Professional Mechanical, Aerospace, and Biomechanical Engineers F = ma computation/simulation lab and office hours Day Monday Tuesday Wednesday Friday
Time 5:45-8:45+ 5:45-8:45+ 3:45-5:00+ 3:45-5:00+
Location Peterson 550-126/Atrium Peterson 550-126/Atrium Peterson 550-126/Atrium Peterson 550-126/Atrium
Office hours start Mon. Jan. 14 Note: CAs facilitate simulation labs, interactive classroom participation, and multimedia peer-networking presentations. Note: CAs comprehensively support MIPSI computation/simulation projects (may relate to job/Ph.D. research). Note: Students are expected to help each other. Cookies provided on occasion.
Course description: ME331A, Advanced Dynamics & Computation Vector algebraic/differential geometry for kinematic analysis. Formulation of equations of motion for 3D multibody systems with: Newton/Euler equations; angular momentum principle; and D’Alembert principle (Dynamics road maps); Symbolic and numerical computational solutions to linear/nonlinear algebraic and differential equations governing the configuration, forces, and motion of multiple degree of freedom systems. Training for advanced research and professional work. Course description: ME331B, Advanced Dynamics & Simulation Tensors and mass property calculations. Formulation of equations of motion for constrained 3D multibody systems with: D’Alembert principle (Dynamics road maps); power, work, and energy; Lagrange’s equations; and Kane’s method. Euler parameters/quaternions, specified motion, constraint force/torque calculations, feed-forward control, inequality constraints and/or intermittent contact. Symbolic and numerical computer skills for geometry/kinematic analysis, mass/inertia calculations, forces and motion, and simulation of multi-body dynamic systems. Training for advanced research and professional work.
4
Paul prefers talking in person or by phone rather than corresponding by e-mail (particularly on technical matters).
c 1992-2013 by Paul Mitiguy Copyright
325
Skills and training for advanced research and professional careers Advanced Dynamics focuses on efficient formulation and solution of equations of motion for complex 3D multibody dynamic systems. The course facilitates advanced graduate research and professional work. The ”big picture” is F = ma . This course is detail-oriented with focus on details of F, m, a , the equals (=) sign, definitions, equations, words, precise notation, descriptive language, efficiency of formulation, R , MotionGenesis, etc. computational solution, simulation, visualization, MATLAB Interactive participation and peer/professional networking Class participation is facilitated by the instructor team who ask students to engage in peer instruction, participate in demos, answer questions, and work problems on the board. Learning by design - we appreciate your feedback. The word educate is from the Latin educare - “to draw out” (not “to stuff in”). Please provide suggestions, criticism, content, images, and creative brainstorming about lectures, labs, computation, homework, demos, classroom interaction, office hours, software, hardware, etc. With 150+ classes of experience and a significant financial investment in your education, you are both learning experts and customers.
Grading • Homework & Computation/Simulation Labs: 30% – Work is only accepted in the box at the start of class (not by instructors or under office doors) – Work submitted one lecture day late is penalized 15 points. Work submitted two lecture days late is penalized 35+ points, and is not thoroughly examined. Work submitted more than two lecture days is penalized 55+ points and is not thoroughly examined. – Homework is not accepted after the last day of class. – To accommodate ill or overtired students, or students who need an extension for any other reason, two class homework extensions are permitted during the quarter. For example, a homework due Wednesday may be submitted on Friday without penalty. – Submit your work and answers on separate sheets of paper (not on homework assignments). – Communicate clearly, write neatly, and use only one side of the paper. N N P ∆ v ∆ d – Use detailed notation e.g., NvP . Use = for definitions, e..g., NaP = dt – Homework marked optional does not need to be submitted (no extra credit). – Work must be stapled (not paper clipped, dog-eared, origami, or bubble-gummed) √ √ √ √ √−− – Work is graded: ++ (100), + (93), (85), − (78), (70), or no credit (0). – To maximize office hours, your work is examined – but with deep analysis of few (1-3) homework/computational problems. In-depth feedback of your work is available in office hours. – Homework solutions are not posted. Ask friends and instructors for help. Homework is practice, not a trade secret, and you are encouraged to work with your classmates and instructors. There is a strong correlation between high homework scores and high exam scores - and few reasons to do poorly on homework.
• Midterm & Computation/Simulation: 25% The in-class portion is open-book and open-note. No electronic devices permitted (e.g., no cell phone, computer, calculator, etc.). No makeup exam given. Your computation/simulation questions must be done solo. c 1992-2013 by Paul Mitiguy Copyright
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• Final & Computation/Simulation: 30% The in-class portion is open-book and open-note. No electronic devices permitted (e.g., no cell phone, computer, calculator, etc.). No makeup exam without university authorization. Your computation/simulation questions must be done solo – no communication of any class-related material (lectures, notes, homework, labs, exams, questions, etc.) with anyone other than ME331 instructors. • MIPSI - Team-based Simulation Project: 15% 10% Asking and answering a sensible question. Timely presentation to instructor team. 10% Comprehensible schematics (possibly with photo) and detailed modeling assumptions. 10% Precise description of all physical objects and unit vectors. 10% Concise accurate tabular description of all scalar symbols. 50% Correctness of analysis. Short (2-3 pg.), solid report. Text interspersed with plots. 10% Technical difficulty, physical demonstration, or interesting problem
MIPSI •
Model physical system. Capture the essential components of the physnz
ical system being analyzed and draw a simple sketch of the model. •
Identifiers,
symbols and values, e.g., m, g, L, θ. Name and label relevant parts, e.g., bodies, lengths, angles, etc. Introduce unit vectors. Analytically or empirically determine physical constants.
•
Physics:
•
Simplify and solve. Produce numerical or closed form solutions for the
No
ny LA
A
LB N Acm
Using physical principles, (e.g., F = ma ) formulate equations which relate the identifiers and govern the behavior of the system.
az
ay
qA B
•
R and MotionGenesis. unknown identifiers, e.g., with MATLAB
Bcm
qB
Interpret, design, and control physical system: Generate and com-
bz
by bx
municate results (numbers, plots, animation, virtual-reality, etc.) that are easily interpretable by a non-technical person. Graded material:
Student → Box → Instructors (alphabetize/grade/Coursework) → Student (in
class).
Consult Linus Park for questions about homework/computation/test scores. Verify your scores at https://coursework.stanford.edu each week to ensure no grades are overlooked.
R , MotionGenesis) to avoid tedious calculations, When you choose to use computational tools (e.g., MATLAB make sure you know what the computer is doing (it is not magic). Print out and submit appropriate (do not waste paper) computational files (e.g., .m or .all files) and include both input and output. R Computation and visualization tools (MATLAB , MotionGenesis, Working Model, . . . ) This course provides training for computational tools for generating and solving equilibrium equations. R , MotionGenesis or Excel are useful for generating graphs. Plotting capabilities in MATLAB
c 1992-2013 by Paul Mitiguy Copyright
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Computation/Simulation Labs and Homework Schedule ME331A: Advanced Dynamics & Computation Week 01/06 01/13
1st meeting of week Concepts assigned. Hw 1 due. Basis independent vectors Hw 2 due. Vector computation + - · ×
2nd meeting of week Concepts due. Computation Lab: Mathematics, evaluating expressions, matrices, solving linear/nonlinear algebraic
F=ma
equations. 3D microphone problem. Saving/running .m and .al files.
01/20
Hw 4 due. Vector bases: Rotation matrices I Hw 5 due. Vector differentiation
Computation
Lab:
computation ( +
-
F=ma
nitude), position vectors, rotation
·
Vector × , mag-
matrices, vector geometry (measure-
R r ω v α a
ments of distance, area, volume, angles). Inverse/forward kinematics for neuromuscular biomechanics.
01/27
Hw 6 due. Angular velocity/acceleration
Computation Lab: Symbolic
Direct feedback homework grading - sign up for in-
differentiation, computer solutions to
class time-slot to meet with an instructor.
nonlinear ODEs, SI/US unit conver-
F=ma
sions. ODEs, simulation, plotting for
R r ω v α a
02/03
precessing gyro and torque-free satellite. Automating .m files.
Hw 8 due. Points: Velocity/acceleration I
Computation Lab: Kinemat-
F=ma
ics, angular velocity/acceleration, velocity/acceleration. Trim solution of
R r ω v α a
02/10 02/17
aircraft. Phugoid mode simulation.
Hw 9 due. Points: Velocity/acceleration II Hw 11 due. Particles: mv, 12 mv2 , F = ma
Midterm & Computation Computation Lab: Computer-
Projectile motion of baseball (with/without air-
generated equations of motion (F =
resistance).
ma ). Accuracy (closed form vs nu-
Vibration/damping/resonance
of
mass/spring/damper rocket-slide ride.
merical solution) of ODEs.
F=ma
lation, plotting, and visualization of projectile motion and rocket-sled.
R r ω v α a
02/24
03/03
03/10
Hw 17 due. Translation: Laws of motion Computation: Coast-guard helicopter rescue
Computation Lab: Forces and motion, muscles, indeterminate sys-
F=ma
tems. Inverse/forward dynamics for neuromuscular biomechanics.
Hw 12 due. Mass/inertia I Simulation Project: MIPSI Hw 14 due. Rigid body momentum, energy, motion Consulting – submit question, model, system picture, identifier table. In-class Dynamic Celt Lab Hw 18 due. Systems: Road maps/DAlembert’s method Simulation Project: MIPSI Road maps and cyber-knife surgical robot Presentation - submit 1 power-point slide with: (a) question, (b) picture
F=ma
of system, (c) picture of team, (d) results (answer to question).
03/17
Simu-
Final exam. MIPSI Project - Team Simulation Report Grades in Axess. Course evaluations.
March 25-31 Spring break c 1992-2013 by Paul Mitiguy Copyright
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ME331B: Advanced Dynamics & Simulation Week 03/31 04/07
04/14
1st meeting of week
2nd meeting of week
Advanced position vectors and geometry
Road-maps with constraints
Hw 3 due. Advanced vector geometry, vector loops,
Simulation Lab: Computer gen-
gradients, integrals over curves/surfaces.
erated static/dynamic equations for
Hw 21.2, 3 due. Four-bar linkage statics and dy-
constrained multibody system. Initial
namics (holonomic constraints/closed-chains).
values from nonlinear algebraic equa-
Effi-
ciency of road-maps vs. single free-body diagrams.
tions. Constraint stabilization.
Hw 10.1-15 due. Constraints I (do Optional)
Simulation Lab: DAEs. Con-
Configuration/motion
tinuous solutions to nonlinear al-
variables/constraints
(holo-
nomic/nonholonomic). Degrees-of-freedom.
gebraic equations.
Linkage analy-
sis/design. SkyCam.
04/21
Hw 10.16-end due. Constraints II (do Optional) Rolling, wheels, gears, bowling-ball, top, football, rat-
piston
Midterm & Simulation
tleback, constant-speed gear, hexapod, tether, cam.
04/28
05/05 05/12
Midterm Simulation due R , , ... Sim tools: MATLAB
Hw 7 due. Euler parameters & quaternions. Poisson & Rodrigues parameters, rotational ODEs
Hw 20 due. Kane/Lagrange I – unconstrained (no Optional). Simulation Lab: Efficient formulation and solution for F = ma .
Kane/Lagrange methods.
Hw 21 due. Kane/Lagrange II – with constraints
Simulation Lab: Nonholonomic
(no Optional) Generalized coordinates/speeds. Par-
constraints.
tial velocity, virtual displacement. Kinetic energy, ef-
rattleback.
Rolling disk, spinning gears, ropes/contact
fective force.
05/19 05/26
Feed-forward model-based control of multi-body sys-
Simulation Lab:
tems (with/without constraints)
Feed-forward model-based control
Hw 22 due. Feed-forward control
Simulation Project: MIPSI
Optional: Hw 12. Advanced mass & inertia.
Consulting – submit question, model, system picture, identifier table.
06/02
Simulation Project: MIPSI. Selection for
Final exams start
exam - submit 1 power-point slide with: (a) question, (b) picture of system, (c) picture of team, (d) answer.
06/09
Final simulations (3). MIPSI Project - Team Simulation Report Grades in Axess. Course evaluations.
June 16 Graduation
⇒
Jobs/Ph.D.
MIPSI simulation team projects Spring 2012 Feed-forward model-based control of SkyCam Feed-forward control of spacecraft with quaternions Feed-forward model-based control of “smart lamp” Feed-forward model-based control of rolling disk Art & Engineering: Motion of rotary pintograph
Take-off torque and trajectory of XV-22 Dynamics of aerial refueling hose whip Dynamics of active vehicle suspension Aerodynamics of flap-winged aircraft Rollover rate of 3-wheeled vehicle
Dynamics of a golf swing Gear train dynamics Can a ball roll uphill? Rolling ball in vertical tube
Future topics and computation/simulation labs for ME331C: • Kane+ : Constraint forces, augmented (simulation) and embedded (controls) methods • Integrals of equations of motion (generalized principles of conservation of energy/momentum). • Linearization of equation of motion for classic control-system design. • Robotics: redundancy/singularities and path planning. • Numerical methods: Integrators, inequality constraints, event-handling • Efficient formulation of equations of motion for systems with gyrostats. • Contact detection, collisions, contact response, friction, event-handling • Force, torque, replacement, impulse, stress, strain, flexibility • Dynamics and control of systems with flexible bodies (constraints and Order-N) R • Skilled integration with CAD, FEA, and controls (SolidWorks, MATLAB , Simulink, . . . ) c 1992-2013 by Paul Mitiguy Copyright
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Graduate Dynamics Syllabus Date 1/06 Wed
1/08 Fri
Who P
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Assignment Topic Concepts assigned Music: TBD. Course introduction. What is “dynamics” and who cares: Physics, mechaniHw 1 assigned cal, aerospace, and biomechanical engineering. MIPSI problem solving methodology. Course Hw 2 assigned roadmap: F = ma . Demo: Babyboot and MotionGenesis. Distribute textbooks. Math Chapters 1, 2, 4 review: Trigonometry (circles, triangles, sine, cosine) and calculus (differentiation). The importance of definitions: the definition of π; how to calculate a value for π?. Definitions of sine/cosine; derivatives of sine/cosine to complete blank in notes. Review of differentiation R . Install and solving nonlinear algebraic equations with MotionGenesis and/or MATLAB MotionGenesis and PlotGenesis from course website. Why use a symbolic manipulator R , like MotionGenesis? (or related computer programs, e.g., Mathematica, Maple, MATLAB Working Model, or MSC.Adams). Concepts due Music: TBD. TA: Class photos/names. The importance of definitions: the definition Hw 4 assigned of π; how to calculate a value for π?. Definitions of sine/cosine; derivatives of sine/cosine to Chapter 5 complete blank in notes. Solve x2 − cos(x) = 0. (solution is ≈ ± 0.824). Reminder: Use a computer to solve nonlinear equations (e.g., Homework 2.17). Who invented vectors and when? Basis independent vectors and vector operations. Differences and similarities between vectors and column matrices. Kane’s 2nd theorem “Everything is equal to everything else”. Review of dot, cross, and derivatives of vectors in Concepts in Newtonian mechanics. The righthand rule as a universally accepted convention? Properties of dot/cross b(a · c) −c(a · b) and a · b ×c = a × b · c. Dot-products and vector magnitudes and cross-products via right-handrule, the “clock-method”, and determinants with a single right-handed, orthogonal, basis. Unit vectors as the “I” in MIPSI. Draw examples of unit vectors as sign posts in Section 2.4. When are two vectors equal? (differences between equal position vectors equal force vectors, and equal vectors). Philosophy on applied mathematics - concepts, calculations, context. Philosophy on vectors to supplement/replace geometry/trigonometry in high-school. Conceptual introduction to dyads, dyadics, triads, triadics, and tensors. Helpful hints for Hw 2. Vector basis and basis vector. Bases, spanning, linear independence, and locating points in R1 , R2 , R3 . The importance of words: Orthogonal, unitary, dextral basis (and the language, history, culture, and biology/genetics of right and left). Coordinate systems: [Cartesian (demo: ball in space), Polar/cylindrical (demo: ball in can), Spherical (famous spheres and singularities - demo: basketball)], generalized coordinates (position variables), distance and angle. Why generalized coordinates make me happy. Bases vs. coordinate systems.
1/13 Wed
P
Hw 1 due Hw 2 due
The point of each Hw 2 problem. How to remember a basis, dude. Question of the day: What is an angle: Two lines: 0 ≤ θ ≤ 90◦ ; Two vectors: 0 ≤ θ ≤ 180◦ ; Three vectors: -180 ≤ θ ≤ 180◦ . Rotation matrices (and coordinate systems). Demo: Why use rotation matrices - a spiraling wobbling football. Successive rotations and the babyboot in Section 5.5. Student Demo: Efficiency of transpose versus inverse for rotation matrices. Dot-products (and vector magnitudes and angles between vectors) and cross-products with multiple right-handed, orthogonal, bases. “Everyone has an angle” - application specific Euler angles in Section 8.3. Demo of “roll, pitch, yaw” and “rotation, obliquity, and torsion” and their dependence on rotation order. Appendix of rotations. Differences between clinical angles and Euler angles. Angles and the design of the XV-22 aircraft. Simple θ λ rotations. Who invented Euler parameters and quaternions and when? Euler parameters and quaternions (analogy to imaginary numbers). Rotation matrices (direction cosines) vs. transformation matrices. MotionGenesis: BasisSubscripts, RigidFrame, RigidBody, Rotate. Why we take pictures: Love thy neighbor. Pat Forrester (NASA astronaut), Jerry Yang and Dave Filo (Yahoo), Naveed Hussain (Boeing Chief), Salma Saeed (Lockheed Chief), Keith Reckdahl (Loral/Lockeed guru), Scott Delp (Biomechanics), Bob Ryan (CEO ADAMS), Keith Buffinton (Dean/Bucknell), Charles Wampler (GM Chief Scientist), TA Robert Usiskin (JPL), TA Andrew Reid (FMC), Student 2008 Brenda Scheufele (Tufts/F18 Pilot), . . . .
1/15 Fri
P
Hw 5 assigned Chapter 6
Helpful hints for Hw 4. Similarities and differences between vector bases and reference frames. Demo: Comparison of textbook definitions of vector differentiation (do you need a reference frame?) The definition of the derivative of a vector (the slow way to calculate a derivative). A A A A A A A dv = dv1 a + v da1 + dv2 a + v da2 + dv3 a + v da3 1 1 2 2 3 3 dt dt dt dt dt dt dt Question of the day: What is the most important formula is kinematics? Demo: Using a bike-pump to demonstrate the derivative of a vector. Demo: how does v1 change in A (without light-speed relativity). How does the unit vector a1 change in magnitude in A. How does the unit vector a1 change in direction in A. The golden rule for vector differentiation ($1,000,000 formula) as a definition of angular velocity. Calculating derivatives of vectors with MotionGenesis. Helpful hints for Hw 5.
1/20 Wed
P
Hw 4 due Hw 5 due Hw 6 assigned Chapter 7
1/22 Fri
P
Hw 8 assigned Chapter 10
1/27 Wed
P
Hw 6 due
The symbol, name, and definition for Aα B and huh? Question of the day: Does a point have angular velocity? (Question asked by Thomas Kane to Bernie Roth’s during Bernie’s interview for a professorship at Stanford). Early commercial multi-body programs (e.g., Working Model) and their language for coords/points. How does one find angular velocity (a vector quantity) from a rotation matrix or Euler angles/parameters (scalars)? Worked out angular velocity and angular acceleration examples for babyboot and spinning book (with demo). Calculating angular velocity using basis vectors and rotation matrices. Simple angular velocity. Angular velocity addition theorem. Setting and getting angular velocity and acceleration with MotionGenesis. Demo: Comparison of definition of angular velocity with other textbooks. Marcelo Crespa da Silva (et. al) say ”The [golden rule of vector differentiation] is of fundamental importance in dynamics ... as it is used by all dynamicists.” Check out the “angular velocity of a point” lie at http://en.widipedia.org/wiki/Angular velocity. Demo: Spinning bicycle wheel and angular velocity weirdness. Helpful hints and the point of Hw 5 and Hw 6. Question of the day: What is a point and what are its properties? The symbol, name, and definition for NaQ and huh? The pictures and proofs for the four formulas for velocity. The direct relationship between acceleration formulas and velocity formulas. Differences in human intuition between velocity and acceleration. Definition of velocity, position, and distance. Geometry, the Greeks and Gibbs. The Summary of Equations Toolbox. Worked out velocity examples in book. Setting and getting position vectors; setting velocities and accelerations via definition with MotionGenesis. Knowing when a vector can be differentiated. Checking if the right-hand side of an equation (e.g., v2pts) is valid for all time. Using v1pt and v2pts to efficiently calculate the velocity of a point at an instant. Mathematical parallels between velocity (intuitive) and acceleration (not so intuitive). Special acceleration names - transport, centripetal, relative, tangential, and Coriolis. Using the Greek roots of “pet” (e.g., petition means seeking a request, competition means seeking a goal) and “fugal” (e.g., fugitive means fleeing from bad situation) to remember centripetal and centrifugal. Worked out acceleration examples in book. Demo: Swinging spring. Knowing when to surrender to a computer. Setting velocity and acceleration via v1pt and v2pts with MotionGenesis. Kinematics Toolbox Formulas. Helpful hints for Hw 8.
1/29 Fri
P
2/3 Wed
P
2/5 Fri
P
2/10 Wed
P
Hw 10.2, 3, 4, 5 assigned Types of constraints, position (orientation/angles and position); velocity (angular velocity Hw 11.2-Hw 11.10dand assigned velocity); acceleration (angular acceleration and acceleration). Definition of degrees of Chapters 11, 12 freedom in terms of motion (not configuration). Constraints and limiting degrees of freedom of particles and bodies. Use of redundant position variables for planar pendulum and spherical pendulum as an analogy to Euler parameters. Mathematical description of rod, rope, and ball joint. Motion constraints as derivative of configuration constraints - but inability to integrate certain motion constraints to find configuration constraints holonomic/nonholonomic. Question of the day: What is rolling and what is its mathematical description? Question of the day: Do all balls roll the same (or downhill)? What is contact? The three points of contact (contact points and path point). Demo: Screws and clamps (constraint relating rotational motion to translational motion. Demo: The string-pendulum as unilateral constraints. Demo: The geometry of objects that roll and objects that do not (concave/convex/differential geometry). Demo: Rolling spheres (ball bearings), rolling disks (wheels), and footballs. Demo: Ball bearings, revolute joint, and torsional spring in coupled two-DOF system. Demo: Squiggle ball with revolute joint/motor and slot. Constraints. Demo: No-twist joint, stepper motor. Specified force vs. specified configuration, motion, or agitation. Hw 8 due Helpful hints for Hw 10. Setting constraints in MotionGenesis. Demo: Piston problem with Working Model and MotionGenesis. Simulation vs. animation. Gear problems. Demo: Well’s Fargo gears and Kane’s constant-speed gears. Demo: Flywheel car with gears. Demo: Gears, cams, and dancing robots. Two, three, and four gear simulations with Working Model. position,velocity, and acceleration variables. Generalized speeds, partial velocities and angular velocities, virtual displacements and virtual angular displacements. Demo: Rolling ball in can. Kinematics Toolbox Formulas. Expectations for Midterm and MIPSI project. Part of Hw 10 due Midterm exam Part of Hw 11 due Midterm
2/12 Fri
P
Remainder of Hw 11 Midterm assigned. solutions. Question of the day: What is a particle what are its properties? Question Chapter 13 of the day: What is mass? Etymology of the word “mass”. Reading: Pgs. 163-168 of Bill Bryson’s A Short History of Nearly Everything. What is space and time? Human, Ocean (1 mile deep), Billiard ball (Earth - 7900 mile diameter), Sun (109 x diameter of Earth) Orbit (3 km compared to billiard ball). More than 99.9% ( 4999 5000 ) of mass is concentrated 1 ) of the volume. It in an atom’s nucleus whereas the nucleus is on one billionth ( 1000000000 23 takes 6.023 x 10 atoms to make up 1 gram of hydrogen (the most plentiful substance in the observable universe). but there is only an estimated 6.023 x 1080 atoms in the entire observable universe! Definitions of linear, angular, and generalized momentum. Demo: Determination of mass center by sliding sticks under non-uniform block. Demo: Determination of mass center by rotating rods under block. Demo: Determination of mass center by hanging a tennis rack at various points. Demo: Determination of mass center by trajectory of various points of spinning tennis racquets. Controversy on the definition of angular momentum. Definitions of effective force, moment of effective force, and generalized effective force. In class: Combining symbols worksheet. Demo: Centrifugal force (or centripetal acceleration) via spinning toy with quarter and ball bearings (spin - do not blow!). Demo: Effective force and harmonic forcing of air-conditioner on leaf-spring/damper. Getting linear/angular momentum, kinetic energy, and other particle properties with MotionGenesis. Scalars, vectors, dyadics, triadics, and higher-order polyadics and tensors. Language: Colicky baby, conjunctivitis, infinitesimal, quantum. Invariant, contravariant, and covariant basis vectors in Euclidean R3, tangent and cotangent bundles on manifolds. Introduction of dyads and dyadics from Chapter 2. Forming a dyadic by multiplying two vectors. Analogy between 3×1 column matrix and vectors and 3×3 matrices and dyadics. The unit dyadic and the 3×3 identity matrix. Dot-multiplication of a vector with a dyadic. Definition of inertia dyadic, inertia matrix, moment of inertia, and product of inertia of a particle. Controversy on the symbol, definition, and names for product of inertia.
2/17 Wed
P
2/19 Fri
P
2/24 Wed
P
Remainder of Hw Definition 11 due of a system and a set. Definition of center of mass. Demo: Balancing coke can. Skip Hw 13 Demo: Balancing forks and burning toothpick on wine glass. Demo: Ernest the BalancChaping Bear (static analysis). Demo: Balancing bird. Demo: Balancing large nails on single ters 13,14,15 nail. Experimental and analytical determination of mass, center of mass, and inertia propHw 12 assigned erties. Demo: Ring and disc inertia. Demo: Rolling soup cans. Demo: Ring and disc Hw 14 assigned inertia. Demo: Determination of center of mass via trajectory of various points on a spinning Chapter 17 tennis-racquet. The language of ”spinning about the c.m.” and “spinning about a point”. Physical insights into moments and products of inertia. Physical significance of the inertia dyadic and inertia matrix as a “suitcase”. Setting and getting mass distribution properties in MotionGenesis. Helpful hints for Hw 12. Demo: Squiggle ball with revolute motor and offset-mass center and products of inertia. Formulas for systems of particles (or bodies). Extending F = ma to the translation of systems of particles. Extending F = ma to the translation of a rigid body. Extending F = ma to rotations of rigid bodies (Euler’s equation). Summary of formulas for particles, systems of particles, and rigid bodies with extension to gyrostats. Getting linear/angular momentum, kinetic energy, and other rigid body properties with MotionGenesis. Demo: Metronome and experimental determination of moment of inertia. Demo: Spin stabilization with gyroscope. Demo: Spinning book and moments of inertia. Demo: Spinning a football to stand it upright. Demo: Rattleback LAB and products of inertia. Parallels in formulas between momentum and effective force. A short history of Euler and mechanics Demo: compound pendulum. Helpful hints for Hw 14. F = ma for the classical particle pendulum Demo: Classical and spherical particle Hw 12 due Hw 14 due pendulum. Fundamental laws of 3D rotational motion. Euler T = Iα ? Demo: Rocking sailboat. Generalized effective forces and constraints. MotionGenesis and vehicle skid analysis. Demo: Vehicle skid.
2/26 Fri
P
3/3 Wed
P
3/5 Fri
P
Skip Hw 15 The symbol and words for forces (contact/distance for non-relativistic engineers and fundamenPart of Hw 16 assigned tal forces for quantum physicists). Question of the day: What is a force? (Feyman) The lack Hw ?? assigned of definition and large number of equations for a force. The philosophy and science of forces. Part of Hw ?? assigned Definitions of science. Controversies in evolution and gravity. Forces, impulses, moments, Part of Hw 19 assigned torques, resultant, and replacement. Forces: gravity, translational springs and dampers, linear Chapters 18,19,20,21,23,24 actuators. Relationship of force to electrical current in linear actuators (motors). Demo: Bike pump as nonlinear spring/damper. Springs in parallel and series. Demo: Slinky. Demo: Torsional spring exerciser. Demo: Torsional spring/damper in MSC.Software notepad. Moment of a force, replacing a set of forces with a simpler equivalent set (modeling). Torques: rotational springs Demo: metronome, Torques: rotational dampers, motors. Relationship of torque to electrical current in a rotational motor. Demo: Spinning motor, back-EMF. Controversy on the aerodynamics of a baseball. Gravity and the equivalence principle. Question of the day: What is potential energy? Potential energy and work. Impulse-momentum. Coefficient of restitution. Demo: Happy Balls. Part of Hw 16 due Helpful hints for Hw 15. Demo: Eddy current tube (magnetism). Demo: Wilbur force Hw ?? due pendulum (coupled springs). Demo: The popper as stored potential energy. Part of Hw ?? due Part of Hw 19 due Hw 17 assigned Hw 18 assigned Fundamental laws of translational motion for a particle, rigid body, or system. Aristotle Chapters 22,27, F = mv ? Demo: Nerf football. Newton F = d (mv ) or F = ma ? Solutions for projectile dt 28 motion with and without air-resistance. Understanding various methods through the classical particle pendulum. Power/Energy-rate principle for one DOF problems. Demo: Energy exchange for translational motion with slinky and person-particle. Demo: Harmonic forcing with a Scotch Yoke. Demo: Energy exchange for rotational motion with powerbee. Related and other advanced methods for forming equations of motion - LaGrange, Kane, D’Alembert, Hamilton, Order-N.
3/10 Wed
P
3/12 Fri
P
3/17 Wed
P
Hw 17 due Hw 18 due
Final
Demo: ConservationOfAngularMomentumHuh.wm2d. Demo: Rolling disk simulation with MotionGenesis and Animake. Discussion of spin stabilization vs. rolling for riding a bike (particularly on ice). Helpful hints for Hw 20. Demo: AirConditionerWithDamping.wm2d. Demo: AirConditionerSimple.wm2d. Demo: EccentricParticleAirConditionerForcedVibrationKane.al. Demo: ParticleOnSpinningSlotKane.al. Demo: InvertedPendulumOnCartDynamics.al. Demo: SpinningBookFBD.al. Demo: SpinningBookKane.al. Demo: SpinningBookLagrange.al. Demo: BabybootWithKanesMethod.txt. Demo: SingleWheelTrailer.al. Demo: Explorer I and spinning condensed milk. Demo: Spinning to stand-up a football. Helpful hints for whose equations to use where. The needs for doing problems to build up your “dynamics muscle”. Last day of class. What are equations of motion good for? Discussion of linearization, stability, control, simulation, and design of equipment. Demo: Rolling disk and Euler’s disk experiment, MotionGenesis, and Animake. Advanced topics: auxiliary generalized speeds and constraint forces. Impulse-momentum. Demo: KEGainImpulseMomentum.wm2d. Demo: Astro Blaster. Demo: Ernest the balancing bear. Energy and momentum integrals of the equations of motion. Linearizing equations of motion. Feed-forward control (computed torque). CAD/CAE and other commercial simulation software. Modeling flexibility with flexible beams and FEA modes. Working Model simulation of windmill and truck driving over bridge. Demo: Ernst the Balancing Bear. Demo: vN4DPropellor.mpg and creating appealing animations. Demo: MSC2001KickoffVideo2Full.mpg and industry applications. Powerpoint presentation of advanced topics. Demo: Reflecting on dynamics with BeerJohnstonMovie.avi. Ten Commandments of 3D dynamics. Final exam 12:15-3:15 in room to be announced. Demo: Its Easy song.
