Syllabus, Lecture Videos and Lecture Notes
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Detailed Syllabus
(with links to lecture videos)
1. Introduction and Organization
1.1. Introduction: Applications and Examples of Dynamics and Vibrations
1.2. Course Outline
1.3. Course Organization
1.4. Demonstrations
2. Describing Motion of Particles
2.2. Position-Velocity-Acceleration in Cartesian Coordinates
2.2.1. Position
2.2.2. The Inertial Basis
2.2.3. Velocity
2.2.4. Acceleration
2.2.5.
Special
case 1D motion;
Formula
for acceleration in terms of position & speed
2.3. Math Review solving differential equations using separation of variables
2.4. Example: Straight Line Motion with constant acceleration
2.5. Example: Toronto Airport Walkway
2.6. Example: Straight Line Motion with variable acceleration (aircraft take-off distance)
2.7. Integrating/differentiating position/velocity/acceleration measurements with MATLAB
2.8. Math Review Basis vectors and vector components
2.9. Circular motion at constant speed (Cartesian and normal-tangential coordinates)
2.10. Example: Interpreting accelerometer data from an inertial platform
2.11. Circular motion at arbitrary speed
2.12. Example: Vehicle accelerating around a curve
2.13. Motion along an arbitrary planar path with normal-tangential coordinates
2.14. Example: Reconstructing a path from acceleration data
2.15. Analyzing motion using cylindrical-polar coordinates
2.16. Example: Using polar-coordinate formulas
· (Newton’s laws in non-inertial bases)
3. Analyzing particle motion using Newton’s laws
3.2. Calculating forces on particles with known motion
3.2.1. Example: Tablecloth trick
· Review of forces at contacts (Normal and Friction Forces)
3.2.2. Example: Calculating maximum acceleration of a people mover
3.2.3. Example using n-t coordinates: aircraft in a standard rate turn
3.3. Predicting the motion of particles subjected to known forces
3.3.1. Example: trajectory formulas with no air drag
3.3.2. Example: ‘Shoot the monkey (or Elmo)’
3.3.3. Example: Analyzing motion of a suspension
· Equation for forces exerted by a spring
· Solution using MATLAB ‘Live Script’
· Solution using ‘ode45’ in MATLAB
3.3.4. Example: centrifugal pump (using polar coordinates)
3.3.5. Example: trajectory of a flying squirrel (MATLAB ode45 with ‘event’ function)
· Discussion of ‘Event function’
3.3.6. Example: predicting motion of a 2-storey building using MATLAB ode45
3.3.7. Example: Quadrupole filter
4. Conservation laws for particles
4.1. Power-work-kinetic energy relations for a single particle
4.1.1. Definitions of power and work
4.1.2. Definition of kinetic energy
4.1.3. Power-work-kinetic energy for a particle
4.1.4. Example: calculating power of a force
4.1.5. Example: Calculating work done by a force
4.1.6. Example: Calculating force from work
4.1.7. Example: Using power-KE relation to calculate average acceleration of a vehicle
4.1.8. Example: Power calculations for an electric aircraft
4.1.9. Example: using work-KE relations to design a crumple zone
4.2. Energy relations for conservative systems of particles
4.2.1. Conservative, non-conservative and workless forces
4.2.2. Potential energy of a conservative force
4.2.3. Example: calculate potential energy of planetary gravity
4.2.4. Example: Forces induced by the ‘Cheerio effect’
4.2.5. Table of potential energies for common forces
4.2.6. Energy equation for a conservative system
4.2.7. Example: Energy analysis of a pendulum
4.2.8. Example: Energy analysis of a spring-mass system
4.2.9. Example: Design a dynamic climbing rope
4.3. Impulse-Momentum relations for a single particle
4.3.1. Definitions of linear impulse and linear momentum
4.3.2. Impulse-Momentum relation for a single particle
4.3.3. Example: Calculate the impulse of a model rocket motor
4.3.4. Example: Estimate jump height from a force-plate measurement
4.4. Impulse-Momentum relations for a system of particles
4.4.1. Total momentum of a system by summation and using center of mass
4.4.2. Impulse-momentum relation for a system
4.4.3. Example: estimate the recoil velocity of a rifle
4.4.4. Example: dog-in-a-boat
4.4.5. Example: design padding for a crash helmet
4.5. Analyzing Collisions
4.5.1. Restitution Coefficient
4.5.2. Straight line motion collision formulas
4.5.3. Example: experimental measurement of restitution coefficient of granite spheres
4.5.4. Example: calculating restitution coefficient from the impulses during a collision
4.5.5. Example: measuring restitution coefficient by timing bounces
4.5.6. 3D restitution coefficient formula for frictionless collisions
4.5.7. 3D collision formulas
4.5.8. Example: Oblique collision of two spheres
4.5.9. Example: How to get rich using collision formulas
4.5.10. Example: ‘Spot the ball’ after a collision
4.6. Angular Impulse-Angular Momentum relations for particles
4.6.1. Definitions of angular impulse and angular momentum for a particle
4.6.2. Angular impulse- Angular momentum relations for a single particle
4.6.3. Example: calculating speeds of a satellite at apogee and perigee
4.6.4. Example: critical speeds for tipping a baby-walker
4.6.5. Angular momentum of a system of particles
4.6.6. Angular impulse-angular momentum relations for a system of particles
4.6.7. Example: calculate impact speed required to break a diatomic molecule
5. Vibrations
5.1. Features of a typical vibration response
5.3. Example: Quantifying a measured harmonic motion
5.4. Free Vibrations of un-damped systems
5.4.1. Vibration of a 1 degree of freedom system: The Harmonic Oscillator
· Solving the EOM using tabulated solutions
· Deriving the solution to the EOM
5.4.2. Vibration of systems with several DOF
5.4.3. Counting degrees of freedom and vibration modes for a vibrating system
5.4.4. Examples of counting DOFs and natural frequencies
5.4.5. Example of calculating a natural frequency: the friction oscillator
5.4.6. Example of calculating a natural frequency: a floating buoy
5.4.7. Short cuts for calculating natural frequencies: combining springs
5.4.8. Short cuts for calculating natural frequencies: using energy to derive an EOM
5.4.9. Calculating natural frequencies of nonlinear systems (pendulum)
5.4.10. Example: natural frequency of the ‘minus-k’ vibration isolation system
5.4.11. Example: natural frequency of an anti-resonant vibration isolator
5.5. Free vibration of damped systems
5.5.1. Modeling energy loss: the dashpot
5.5.2. Free vibration of a damped 1DOF system
5.5.3. Summary of constants used in formulas for damped vibrations
5.5.4. Example: calculating damping ratios for a simple spring-mass system
5.5.5. Example: Design a thrust stand
5.5.6. Example: Modeling an impact as free vibration of a damped spring-mass system
5.5.7. Measuring natural frequency and damping coefficient from an impulse test
5.6. Forced Vibrations
5.6.1. Externally forced damped harmonic oscillator
5.6.2. Example: predict the amplitude of vibration of a forced system
5.6.3. Example: predict the influence of changing damping in a system on its vibration
5.6.4. Example: calculate the bandwidth of a force sensor
5.6.5. Using external forcing to measure natural frequency and damping coefficient
5.6.6. Forced vibration of systems with several DOF
5.6.7. Base excited damped harmonic oscillator
5.6.8. Example: Find the amplitude of vibration of an isolation table
5.6.9. Example: Design a suspension system
5.6.10. Rotor excited damped harmonic oscillator
5.6.11. Example: Fix a vibration problem
5.6.12. Example: Balance a wind turbine
5.6.13. Example: Analyze the anti-resonant vibration isolator
6.1. Describing motion of rigid bodies
6.1.1. Describing 2D rotations
6.1.2. Example: find a 2D rotation matrix
6.1.3. Describing 3D rotations
6.1.4. Example: find a 3D rotation matrix
6.1.5. Angular velocity and angular acceleration
6.1.6. Example: find angular velocity of an aircraft and propeller
6.1.7. Spin tensor and the rotation-angular velocity formula
6.1.8. Example: Find spin tensor for a 2D rotation
6.1.9. Formulas for relative velocity and acceleration of two points in a rigid body
6.1.10. Example: velocity and acceleration of points on a spinning disk
o Derivations of formulas in Sect 6.1 (optional)
6.2. Analyzing motion in systems of rigid bodies
6.2.1. Example: analyze a simple robot arm
6.2.2. Example: analyze motion of an oil jack
6.3. Gears, pulleys and the rolling wheel
6.3.1. Simple gear pair
6.3.2. Example: calculate transmission ratio for a wind turbine gearbox
6.3.3. Pulley pairs
6.3.4. Epicyclic gears
6.3.5. Example: Calculate angular speeds in an epicyclic gear
6.3.6. Rolling wheel formulas
6.3.7. Example: Kinematics of the ‘inerter’
6.4. Inertial properties of rigid bodies
6.4.1. The inertia matrix (tensor) of a system of particles or rigid body
6.4.2. Example: calculate the inertia matrix for a simple system of particles
6.4.3. Angular momentum and KE in terms of the inertia matrix
6.4.4. Example: calculate angular momentum and KE of a simple system of particles
6.4.5. Example: calculate the mass moment of inertia matrix for a cone
6.4.6. Tables of inertia matrices (about COM) for common 3D objects
6.4.7. Changes to the inertia matrix resulting from a rotation
6.4.8. Understanding the mass moment of inertia
6.4.9. Simplified formulas for angular momentum and KE for 2D problems
6.4.10. Example: calculate the mass moment of inertia matrix for a triangular plate
6.4.11. Tables of mass moments of inertia for common 2D objects
6.4.12. The parallel axis theorem
6.4.13. Calculating mass moments of inertia of a system of rigidly connected bodies
6.4.14. Example: find the COM and mass moment of inertia of an L section
6.4.15. Angular momentum and kinetic energy of a body rotating about a fixed point
o Derivations of formulas in Sect 6.4 (optional)
6.5. Analyzing rigid body motion
6.5.1. Pure moments/couples/torques; torsional springs
6.5.2. Equations of motion for general motion of a rigid body
6.5.3. Example: analyze an energy storage flywheel
6.5.4. Example: rigid body Olympics: the 1m Race
6.5.5. Example: predict force-acceleration relation for an inerter
6.5.6. Friction forces acting on rolling and sliding wheels
6.5.7. Example: reversal of motion of a slipping wheel
6.5.8. Simplified method of analysis for fixed axis rotation problems
6.5.9. Example: inverted pendulum stabilized by torsion spring
6.5.10. Example: find the center of percussion of a baseball bat
6.6. Work-energy relations for systems of rigid bodies
6.6.1. Example: using energy to predict an angular velocity
6.6.2. Example: analyze the ASTM test for the sweet spot on a baseball bat
6.6.3. Example: find the torque needed to drive an oil jack
6.7. Angular impulse-momentum relations for systems of rigid bodies
6.7.1. Example: the ‘ice skater maneuver’
6.7.2. Example: analyze the ‘yoyo de-spin’ of a satellite
6.7.3. Example: analyze the ‘Cubli’
6.8. Examples of 3D motion of rigid bodies
6.8.1. Example: Precession of a spinning wheel
6.8.2. Example: Predict the path of a boomerang
6.8.3. Example: Tilting a spinning wheel on a turntable
c. Integrals
b. Loops
d. Examples Using Loops, Conditional Statements, and Plotting Graphs and Images
e. Functions
f. Example Problem Featuring a Function, a Loop and a Conditional Statement
3. Solving differential equations with MATLAB
a. Solving a simple differential equation by hand
b. Solving Differential Equations Analytically with a Live Script
c. Solving Differential equations Numerically with ode45 in a matlab function
d. Example: Solve and Plot the Solution to a Differential Equation (Battery Charging)
e. Solving Two Simultaneous Differential Equations (Predator-Prey Problem)
4. How a numerical differential equation solver works
Appendix 2: DESIGN PROJECT 1 Dynamically tuned mass launcher
2. Introduction to the MATLAB optimizers (fminunc and fmincon)
3. How to set up the design calculation with the optimizer
4. Image processing your high-speed video
Appendix 3: DESIGN PROJECT 2 Predator-Prey Contest
2. Setting up equations of motion
3. Using the template code to develop your controller function
4. Suggested predator strategy
5. Avoiding ground and refueling
6. How to prepare and test your code before submitting it
Appendix 4: DESIGN PROJECT 3 Vibration Isolator
Appendix 5: DESIGN PROJECT 4 Solar Car
- Project overview
- Suggested Design/Test Schedule
- DC Motor Equations
- Solar Panel Equation
- Energy Losses
- Design Calculations
- Design Problem 1: Calculating properties of DC motor
- Design Problem 2: Calculating properties of solar panels
- Design Problem 3: Power/Torque curves for motor/panel combination
- Design Problem 4: Analyzing transmission (see also 6.3.1 and 6.3.6 of lecture videos)
- Design Problem 5: Deriving the equation of motion for the vehicle
- Design Problem 6: Solving the EOM with MATLAB