Advanced Classical Mechanics/Solving Problems


 * 1) Read the problem
 * 2) Draw a diagram
 * 3) Identify the degrees of freedom
 * 4) Assign a coordinate to each degree of freedom
 * 5) Calculate $$T$$ and $$V$$ in terms of the coordinates
 * 6) Sometimes $$T$$ is difficult; use Cartesian coordinates or whatever system is convenient
 * 7) Convert to the coordinate system in (4)
 * 8) Look for cyclic coordinates
 * 9) Each one gives you a "first integral".
 * 10) A "first integral" is a first-order differential equation.  It is usually easier to solve than Lagrange's equations which are second order.
 * 11) If only one coordinate remains, you can either
 * 12) Use Lagrange's equations, or
 * 13) Use the conservation of $$H$$ if $$\partial L/\partial t=0$$
 * 14) If more than one coordinate remains, it is often easier to use Lagrange's equations for each of them, because the Hamiltonian usually couples the degrees of freedom.
 * 15) You should have as many equations as degrees of freedom. Solve them!
 * 16) Apply the boundary conditions.