Dynamics

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

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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

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8

Linear and Angular Momentum Principle for Rigid Bodies

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9

Work-energy Principle for Rigid Bodies

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10

Examples for Lecture 8 Topics

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11

Examples for Lecture 9 Topics

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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

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14

Exam 1

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

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18

Examples for Session 16 Topics

Lagrange's Equation of Motion

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19

Examples for Session 17 Topics

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20

Lagrange Multipliers, Determining Holonomic Constraint Forces, Lagrange's Equation for Nonholonomic Systems, Examples

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21

Stability of Conservative Systems

Dirichlet's Theorem

Example

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22

Linearized Equations of Motion Near Equilibria of Holonomic Systems

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23

Linearized Equations of Motion for Conservative Systems

Stability

Normal Modes

Mode Shapes

Natural Frequencies

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24

Example for Session 23 Topics

Orthogonality of Modes Shapes

Principal Coordinates

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25

Damped and Forced Vibrations Near Equilibria

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26

Exam 2

Problem Set 1 (PDF)

Problem Set 2 (PDF)

Problem Set 3 (PDF)

Problem Set 4 (PDF)

Problem Set 5 (PDF)

Problem Set 6 (PDF)

Problem Set 7 (PDF)

Problem Set 8 (PDF)

Problem Set 9 (PDF)

Problem Set 10 (PDF)

Quiz 1 (PDF)

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Quiz 2 (PDF)

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Practice Problem Set 1 (PDF)

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Practice Problem Set 2 (PDF)

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Practice Quiz 1 (PDF)

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Practice Quiz 2 (PDF)

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