Lecture

Recommended Reading from Text

Introduction

1-5

1

Mechanical systems; translational masses, springs, dampers

14-27

Mechanical systems; simple combinations, effect of gravity and static equilibrium.

27-28

Mechanical systems; multiple combinations

29-31

2

Rotational mechanical systems; inertias, springs, and dampers.

31-34

Rotational mechanical systems; simple and multiple combinations, kinematic constraints.

34-37

Mathematical models; input-output variables, classification.

50-56

3

Review for Exam 1

Exam1

Elementary linear algebra; matrices and vectors, matrix operations, matrix inversion.

4

Use of Matlab; script files, programming syntax, matrix operations, data files, graphics.

Handout

State space models; state variables, vector-matrix format, standard form.

57-61

Obtaining a state space model from an input-output format (no derivatives on input).

61-64

5

Obtaining a state space model from an input-output format (derivatives on input).

64-67

Numerical solution using Euler's method; both scalar and vector systems.

108-112

Other methods; checking for accuracy, stiffness.

112-121

6

Numerical solution in Matlab; lsim and ode45

Obtaining a state space model for a nonlinear system

Simulating nonlinear systems using Matlab.

7

Linearization with Taylor's series

Linearizing a dynamic model about the position of static equilibrium.

Introduction to simulations packages; Matlab Simulink

8

Review for Exam 2.

Exam 2

Analytical solution of first order models; free response, step response, time constant.

76-85

9

Analytical solution of second order models, free response, damping ratio and natural frequency

85-91

Analytical solution of second order models; step response.

91-97

Laplace transform and transfer functions.

229-232

10

Obtaining transfer functions for higher order systems.

Review of complex numbers

Handout

Phasor solution of linear, time-invariant ODE's subject to sinusoidal input.

236-237

11

Frequency response of first order systems; Bode diagram, corner frequency.

243-249

Frequency response of 2^nd order system, damping ratio, quality factor, corner frequency

246-249

Frequency response of 2^nd order system continued.

12

Electrical systems; capacitors, inductors, resistors, sources; node and loop laws

150-156

Operational amplifiers, inverting amplifiers, summers, integrators, differentiators.

156-162

Deriving input-output and state space models for electrical systems.

13

Mixed systems; electomechanical coupling

210-211

DC servomotors

Loudspeaker drivers

14

Introduction to thermal systems; conduction, convection, radiation, reservior.

172-177

Deriving input-output and state space models for electrical systems.

177-182

Introduction to dynamics of fluid systems; Bernoulli's law, law of energy conservation

15

Deriving dynamic models for fluid systems.

Review for Final Exam