| 1 |
Course Overview
Single Particle Dynamics: Linear and Angular Momentum Principles, Work-energy Principle |
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| 2 |
Examples of Single Particle Dynamics |
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| 3 |
Examples of Single Particle Dynamics (cont.) |
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| 4 |
Dynamics of Systems of Particles: Linear and Angular Momentum Principles, Work-energy Principle |
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| 5 |
Dynamics of Systems of Particles (cont.): Examples
Rigid Bodies: Degrees of Freedom |
Problem set 1 due |
| 6 |
Translation and Rotation of Rigid Bodies
Existence of Angular Velocity Vector |
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| 7 |
Linear Superposition of Angular Velocities
Angular Velocity in 2D
Differentiation in Rotating Frames |
Problem set 2 due |
| 8 |
Linear and Angular Momentum Principle for Rigid Bodies |
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| 9 |
Work-energy Principle for Rigid Bodies |
Problem set 3 due |
| 10 |
Examples for Lecture 8 Topics |
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| 11 |
Examples for Lecture 9 Topics |
Problem set 4 due |
| 12 |
Gyroscopes: Euler Angles, Spinning Top, Poinsot Plane, Energy Ellipsoid
Linear Stability of Stationary Gyroscope Motion |
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| 13 |
Generalized Coordinates, Constraints, Virtual Displacements |
Problem set 5 due |
| 14 |
Exam 1 |
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| 15 |
Generalized Coordinates, Constraints, Virtual Displacements (cont.) |
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| 16 |
Virtual Work, Generalized Force, Conservative Forces
Examples |
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| 17 |
D'Alembert's Principle
Extended Hamilton's Principle
Principle of Least Action |
Problem set 6 due |
| 18 |
Examples for Lecture 16 Topics
Lagrange's Equation of Motion |
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| 19 |
Examples for Lecture 17 Topics |
Problem set 7 due |
| 20 |
Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples |
Problem set 8 due |
| 21 |
Stability of Conservative Systems
Dirichlet's Theorem
Example |
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| 22 |
Linearized Equations of Motion Near Equilibria of Holonomic Systems |
Problem set 9 due |
| 23 |
Linearized Equations of Motion for Conservative Systems
Stability
Normal Modes
Mode Shapes
Natural Frequencies |
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| 24 |
Examples for Lecture 23 Topics
Orthogonality of Modes Shapes
Principal Coordinates |
Problem set 10 due |
| 25 |
Damped and Forced Vibrations Near Equilibria |
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| 26 |
Exam 2 |
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