PHY 215 Study Guide - Final Guide: Spherical Coordinate System, Reduced Mass, Areal Velocity
Document Summary
L(q, qdot, t)=t-u, t=total kinetic energy of the system, u=potential energy, q=all the coordinates describing the degrees of freedom of the system. Momentum conjugate to q (q is a coordinate dimension such as x) If the lagrangian is independent of a coordinate q If the conjugate momentum to q, pl/pqdot, is conserved H(p, q)=sum over i (pi qdoti-l), pi=momentum conjugate to qi. H=t+u if u does not depend explicitly on velocities or time but only on coordinates. If the hamiltonian is independent of a coordinate q If the conjugate momentum of coordinate q is conserved Two equations for the total energy of an orbit. This must be true for an orbit to be bound. Planets move in elliptical orbits with one focus at the sun. Kepler"s second law, the conservation of areal velocity. Planetary orbits sweep out equal areas in equal times.
