AA242a: Classical Dynamics

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AA242a: Classical Dynamics
“Dynamics” is the study of the motions of the various objects in the world around us and
is a part of mechanics that studies the effects of forces on the motion of a body or system
of bodies. It forms a central part of all engineering and physical sciences and was first
studied by Galileo, who derived the law of motion for falling bodies. In this course, we
will study the motion of systems of particles under the influence of specified force laws,
with the motion’s evolution determined by Newton’s second law. Given certain laws
determining physical forces, and some boundary conditions on the positions of the
particles, our fundamental problem will be to determine the positions of particles at all
times.
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Instructor
Sigrid Close
Office: Durand 264
Phone: 725-2863
Email: [email protected]
Office hours: Tuesdays, 9-10 AM; Thursdays, 9-11 AM
Location and Time
Tuesdays and Thursdays, 12:50 – 2:05 PM
Skilling 80 (auditorium)
Course Assistants
Jose Padial: [email protected]
Office hours: Mondays, 2-4 PM in Durand 393
Alan Li: [email protected]
Office hours: Tuesdays, 2-4 PM in Durand 393
Problem Sessions: Fridays, 3:15-4:05 PM, Huang 018 (Auditorium)
Text
Required: Classical Mechanics (3rd edition) by Goldstein, Safko and Poole. Errata for
up to and including the 6th printing can be found at:
http://astro.physics.sc.edu/Goldstein/
Recommended: Principles of Dynamics (2nd edition) by Greenwood
MATLAB Resources
MATLAB Primer by K. Sigmon:
http://math.ucsd.edu/~driver/21d-s99/matlab-primer.html
MATLAB Documentation:
http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.shtml
Requirements and Grading
Problem Sets (9 total): 30% of grade
• Weekly problem set assignments
• Solutions will be posted at the time of an assignment’s due date in order to
provide immediate feedback. Hence, no extensions or late homework will be
accepted
• Students may work in groups but should write up solutions individually
• To receive full credit on a problem, a problem set must include a reasonably clear
explanation of the method used to obtain a solution.
Midterm test in class: 30% of grade
Final exam: 40% of grade
Important Dates
Midterm test in class: November 2
Final Exam: December 10
Website
Coursework
Proposed Lecture List
I.
Elementary Particles (Goldstein et al., Chapter 1)
a. System of particles
b. Holonomic and nonholonomic constraints
c. D’Alembert’s principle and Lagrange’s equations
II.
Variational Principles and Lagrange’s Equations (Goldstein et al., Chapter 2)
a. Hamilton’s principle
b. Conservation theorems and symmetry properties
III.
Kinematics of Rigid Body Motion (Goldstein et al., Chapter 4)
a. Orthogonal transformations
b. Eigenvalues and eigenvectors
c. Euler angles
d. Finite rotations
e. Coriolis force
IV.
Dynamics of Rigid Body Motion (Goldstein et al., Chapter 5)
a. Tensors
b. Inertia Tensor and Moment of Inertia
c. Euler Equations
d. Gyroscopes
e. Tops
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