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You can find the lecture notes at this link
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Week 1 - Background Material [2]
Summary
Conserved Quantities, Center of Mass Coordinates, Virtual Work, D'Alembert's Equation, Lagrange's Equations
Reading List
- ``Lagrangian Dynamics''
REF: Wells, D. A. 1967, Chapter 1-3.
- ``Classical Mechanics''
REF: Goldstein, H. 1980, Chapter 1.
Problem Set - 21 September 2005 - Answers
Problem 1 - Conical Spiral
Wells : Problem 3.5.
A bead of mass m is constrained to move along a smooth
conical spiral. The radius of the spiral ρ = a z and the
angle along the spiral φ = - b z where ρ, φ and
z are the standard cylindrical coordinates. Find the
equation of motion of the bead.
Problem 2 - Sprung Pendulum
Wells : Problem 3.7.
A pendulum bob of mass m is suspended by an inextensible
string from the point p. This points is free to move along a
straight horizontal line under the action of the springs each having a
constant k. Assume that the mass is displced only slightly
from the equilibrium position and released. Neglecting the mass of
the springs, find the period of oscillation of the pendulum.
Problem 3 - Bead on a Loop
Wells : Problem 3.12
A bead of mass m is free to move on a smooth circular
wire which is rotating with constant angular velocity ω about a
vertical axis perpendicular to the face of the loop and passing
through its periphery. Another bead is moving under the action of
gravity along an identical loop which is stationary and in a vertical
plane. Prove that both beads have exactly the same motion. What
quantity in the equation of motion for the first bead corresponds to
g in the second equation of motion.
Problem 4 - Barbell
Goldstein : Problem 1.10
Two points of mass m are joined by a rigid weighless rod of
length l, the center of which is constrained to move on a
circle of radius a. Set up the kinetic energy of the system in
generalized coordinates.
Last modified: Wednesday, 30 November 2005 12:14:25
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