A cart and a rolling disk are connected by a rigid massless link of length L. The disk rolls without slipping. What's the force in the link? See Problem Set 9. (Figure by Prof. George Haller.)
Course Features
Course Highlights
This course features a student's complete lecture notes, as well as problem setsand exams with solutions.
Course Description
This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems.
LEC # | TOPICS | LECTURE NOTES |
1 | Course Overview Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle | (PDF) |
2 | Examples of Single Particle Dynamics | (PDF) |
3 | Examples of Single Particle Dynamics (cont.) | (PDF) |
4 | Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle | (PDF) |
5 | Dynamics of Systems of Particles (cont.): Examples Rigid Bodies: Degrees of Freedom | (PDF) |
6 | Translation and Rotation of Rigid Bodies Existence of Angular Velocity Vector | (PDF) |
7 | Linear Superposition of Angular Velocities Angular Velocity in 2D Differentiation in Rotating Frames | (PDF) |
8 | Linear and Angular Momentum Principle for Rigid Bodies | (PDF) |
9 | Work-energy Principle for Rigid Bodies | (PDF) |
10 | Examples for Lecture 8 Topics | (PDF) |
11 | Examples for Lecture 9 Topics | (PDF) |
12 | Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid Linear Stability of Stationary Gyroscope Motion | (PDF) |
13 | Generalized Coordinates, Constraints, Virtual Displacements | (PDF) |
14 | Exam 1 | |
15 | Generalized Coordinates, Constraints, Virtual Displacements (cont.) | (PDF) |
16 | Virtual Work, Generalized Force, Conservative Forces Examples | (PDF) |
17 | D'Alembert's Principle Extended Hamilton's Principle Principle of Least Action | (PDF) |
18 | Examples for Session 16 Topics Lagrange's Equation of Motion | (PDF) |
19 | Examples for Session 17 Topics | (PDF) |
20 | Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples | (PDF) |
21 | Stability of Conservative Systems Dirichlet's Theorem Example | (PDF) |
22 | Linearized Equations of Motion Near Equilibria of Holonomic Systems | (PDF) |
23 | Linearized Equations of Motion for Conservative Systems Stability Normal Modes Mode Shapes Natural Frequencies | (PDF) |
24 | Example for Session 23 Topics Orthogonality of Modes Shapes Principal Coordinates | (PDF) |
25 | Damped and Forced Vibrations Near Equilibria | (PDF) |
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