CLASSICAL MECHANICS | |
MEETING TIMES: | M W F 10:10-11:00 AM ROOM: TKH 111 |
INSTRUCTOR: | Dr. Prabhakar Misra |
OFFICE: | TKH 102 (Tel 806-6251); OPFM 112 (Tel 806-4913) |
OFFICE HOURS: | M W F 11:00-12:00 N OR By Appointment |
GOALS AND OBJECTIVES OF THE COURSE:
To provide a thorough background in Newtonian and Lagrangian Mechanics of individualparticles and a system of particles leading to an in-depth treatment of central forces,rigid body dynamics and small oscillations.
COURSE PREREQUISITE:
Physical Mechanics (021-182) at the level of A.P. Arya, Introduction to ClassicalMechanics, Englewood Cliffs: Prentice-Hall, 1990.
TEXT: H. Goldstein, Classical Mechanics, 2nd ed. Reading, Mass.:Addison-Wesley, 1980.
WEEK OF | SUBJECT | |
| 8/24: | Survey of Elementary Principles | |
| 8/31 & 9/9: | Variational Principles and Lagrange's Equations | |
| 9/14, 9/21 & 9/28: | The Two-Body Central Force Problem | |
| 10/5, 10/14 & 10/19: | The Kinematics of Rigid Body Motion | |
| 10/26, 11/2 & 11/9: | The Rigid Body Equations of Motion | |
| 11/16, 11/23 & 11/30: | Small Oscillations | |
| EXAM I: | 9/21 | |
| EXAM II: | 10/19 | |
| EXAM III: | 11/16 | |
| FINAL EXAM: | 12/9 |
GRADING SCHEME | |
| Homework | 15% |
| Exams I, II & III | 60% |
| Final Exam | 25% |
SUGGESTED READING:
1. A.L. Fetter & J.D. Walecka, Theoretical Mechanics of Particles & Continua,New York: McGraw-Hill, 1980.
2. J.B. Marion, Classical Dynamics of Particles & Systems, 2nd ed. New York:Academic Press, 1970.
3. K.R. Symon, Mechanics, 3rd ed. Reading, Mass.: Addison-Wesley, 1971.
OUTLINE OF ESSENTIAL TOPICS OF COURSE MATERIAL:
Survey of Elementary Principles: Mechanics of a single particle and a system ofparticles; Conservation theorems for linear momentum, angular momentum and energy; Centerof mass; Constraints; D'Alembert's principle and Lagrange's equations; Velocity-dependentpotentials; Simple applications of the Lagrangian Formulation.
Variational Principles and Lagrange's Equations: Hamilton's principle; Calculusof variations; Geodesics; Euler-Lagrange differential equations; Lagrange undeterminedmultipliers; Conservation theorems and symmetry properies.
The Two-Body Central Force Problem: Equivalent one-body problem; Equations ofmotion and first integrals; Classification of orbits; Virial theorem; Differentialequation for the orbit and integrable power-law potentials; Conditions for closed orbits;Inverse square law of force; The Kepler problem.
The Kinematics of Rigid Body Motion: Independent coordinates of a rigid body;Orthogonal transformations; Transformation matrix; Euler angles; Cayley-Klein Parameters;Euler's theorem; Finite rotations; Infinitesimal rotations; Rate of change of a vector.
The Rigid Body Equations of Motion: Angular momentum and kinetic energy ofmotion about a point; Tensors and dyadics; Inertia tensor and moment of inertia; Principalaxis transformation; Euler equations of motion; Torque-free motion of a rigid body; Heavysymmetrical top with one point fixed; Precession and nutation.
Small Oscillations: Stable and unstable equilibria; Eigenvalue equationand the principal axis transformation; Free vibration and normal coordinates; Lineartriatomic molecule.
ASSIGNMENTS AND DUE DATES:
There will be a total of 10 homework assignments as indicated below:
HW#1 Lagangian and Lagrange's Equations of Motion Due: 9/9/98
HW#2 Lagrangian and Lagrange's Equations of Motion Due: 9/14/98
HW#3 Variational Principle and Lagrange Multipliers Due: 9/28/98
HW#4 Constraints and Velocity-Dependent Potential Due: 10/5/98
HW#5 Central Force Due: 10/14/98
HW#6 Central Force Due:10/18/98
HW#7 Kinematics of Rigid Bodies Due: 10/26/98
HW#8 Rotation Matrices and Euler Angles Due: 11/9/98
HW#9 Rigid Body Dynamics Due: 11/16/98
HW#10 Small Oscillations Due: 12/3/98
ATTENDANCE POLICY:
Students are expected to attend all lectures, submit the required homework assignmentsand take the three Mid-Term Examinations and one Comprehensive Final Examination.
N.B. Under the American Disabilities Act (ADA) of 1990, ifyou want to be identified as a person with a disability and need accommodation, pleaseadvise me by making an appointment.