MECH 220 - Introduction to Dynamics

Dynamics of particles and rigid bodies in planar and three-dimensional motion. Kinematics; coordinate systems, rotating frames of reference, rotational kinematics of rigid bodies, relative and absolute motion analyses. Kinetics; equations of motion, impulse-momentum principles and conservation of momentum, principle of work and energy and conservation of energy.

Instructor: Prof. James Richard Forbes

Course Overview

MECH 220 introduces the fundamental principles of kinematics and dynamics for particles and rigid bodies. Students learn to model and analyze motion using Newtonian mechanics, energy methods, and momentum principles.

Topics include:

  • Vectors and reference frames
  • Kinematics
  • Newton’s Laws applied to single and multi-particle systems
  • Impulse and momentum
  • Work and energy
  • Power
  • Mass properties of rigid bodies
  • Euler’s equations

Prerequisite and Corequisite Courses

Students are expected to be comfortable with:

  • Calculus
  • Linear algebra
  • Mechanics fundamentals (from PHYS 131)

Prerequisite Courses

  • MECH 215
  • MATH 262

Corequisite Courses

  • MATH 263

Learning Outcomes

By the end of the course, students will be able to:

  • Perform a kinematic analysis by specifying points and reference frames.
  • Apply Newton’s laws of motion to a particle, a system of particles, and a rigid body.
  • Apply impulse-momentum principles.
  • Apply work-energy principles.

Textbooks

There is no required textbook. However, lectures are based primarily on the following references.

  • G. M. T. D’Eleutario and G. R. Heppler, Newton’s Second Law And All That. (In preparation) Cambridge University Press, 2011.
  • D. S. Bernstein, Geometry, Kinematics, Statics, and Dynamics. (In preparation) Princeton University Press, 2013.
  • A. V. Rao, Dynamics of Particles and Rigid Bodies: A Systematic Approach. New York, NY: Cambridge University Press, 2006.
  • N. J. Kasdin and D. A. Paley, Engineering Dynamics: A Comprehensive Introduction. Princeton, NJ: Princeton University Press, 2011.

Additional Resources

  • A. H. J. de Ruiter, C. J. Damaren, and J. R. Forbes, Spacecraft Dynamics and Control: An Introduction. West Sussex, UK: John Wiley & Sons, Ltd., 2013.
  • P. C. Hughes, Spacecraft Attitude Dynamics, 2nd ed. Mineola, NY: Dover, 2004.

Schedule

Week Date Topic Materials
1 Sep/Jan Physical Vectors and Reference Frames

Physical vectors, basis vectors, components of vectors.
2 Sep/Jan Vector operations and the DCM

Dot and cross products, and direction cosine matrices (DCMs).
3 Sep/Jan Euler Angles

Parameterizing the DCM using Euler angles.
4 Sep/Jan Kinematics

Angular velocity, the Transport Theorem, Poisson’s equation, the relationship between position, velocity, and acceleration.
5 Oct/Feb Newton's Laws Applied to a Single Particle

Fundamental laws governing the motion of a single particle.
6 Oct/Feb Forces

Gravitational, spring, damping, friction, and drag forces.
7 Oct/Feb Newton's Laws Applied to Many Particles

Fundamental laws governing the motion of a single particle.
8 Oct/Feb Impulse and Momentum

Linear impulse-momentum relationships and applications.
9 Nov/Mar Work and Energy

Work-energy methods and conservation principles.
10 Nov/Mar Power and Energy Methods

Energy transfer and engineering applications.
11 Nov/Mar Properties of Discrete and Continuous Rigid Bodies

Zeroth, first, and second moment of mass of discrete and continuous rigid-bodies. The Parallel Axis Theorem.
12 Nov/Mar Dynamics of Discrete and Continuous Rigid Bodies

Deriving the equations of motion of discrete and continuous rigid-bodies.
13 Dec/Apr Euler's Equation

Conservation of angular momentum and energy.