Overview
Description
Advanced Newtonian mechanics. Variational principles, Lagrangian and Hamiltonian dynamics, central forces, rigid body motion, canonical transformations, Hamilton-Jacobi theory, small oscillations, and continuous media.
Units
Lecture3
Catalog Details
Offering
Offered: Every Spring
Terms
spring
Attributes
Standard
Learning Outcomes
- successfully utilize Newton’s laws in situations in which the mass of the system is either constant or is not constant.
- analyze the course of a projectile near the surface of the Earth.
- correctly predict the motion of a particle under the action of a central force. Find conserved quantities and use them to construct trajectory equations.
- find equilibrium orbits of particles under the influence of a central force and predict their stability.
- calculate differential and total scattering cross-sections for un-bound particles subject to a central force.
- formulate Newton’s second law from the point-of-view of a non-inertial observer, and use it to predict the motion of a particle.
- use approximation and perturbative techniques to calculate the trajectory of a particle near the surface of the Earth, to include accounting for (in an approximate way when appropriate) the effects of the rotation of the earth and the resistance of the atmosphere.
- develop LaGrange’s equations using either Newton’s second law, variational calculus, or the principle of virtual work.
- use LaGrange’s equations to analyze the constrained and unconstrained motion of particles, and the stability of their equilibrium orbits. This includes the use of appropriate approximation techniques.
- use LaGrange’s equations to write the differential equations of motion for systems of particles.
- use the method of undetermined multipliers to find the forces of constraint for particles subject to constrained motion.
- use Lagrangian and Hamiltonian analyses to find conserved quantities.
- demonstrate understanding of how symmetries in nature lead to conservation laws.
- find normal modes and normal frequencies for systems of coupled oscillators. This includes the use of appropriate approximation techniques for small oscillations. Given initial conditions, predict the future motion of these systems.
- find the inertia tensor and the principal axes for a rigid body. Analyze such objects, to include predicting the condition of their static and dynamic equilibrium.