Advanced Classical Mechanics/Solving Problems
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- Read the problem
- Draw a diagram
- Identify the degrees of freedom
- Assign a coordinate to each degree of freedom
- Calculate and in terms of the coordinates
- Sometimes is difficult; use Cartesian coordinates or whatever system is convenient
- Convert to the coordinate system in (4)
- Look for cyclic coordinates
- Each one gives you a "first integral".
- A "first integral" is a first-order differential equation. It is usually easier to solve than Lagrange's equations which are second order.
- If only one coordinate remains, you can either
- Use Lagrange's equations, or
- Use the conservation of if
- 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.
- You should have as many equations as degrees of freedom. Solve them!
- Apply the boundary conditions.