Problem 3 The Lagrangian of a particle in spherical coordinates is given by 1 L(r, 0, 6; 1, 0, 0) = ¸m[r² + r²ġ² + r² (sin 0)² ¿²] – V(r) . Write down the momenta conjugate to each generalised coordinate. Write down the Hamiltonian and Hamil- ton's equations.
Problem 3 The Lagrangian of a particle in spherical coordinates is given by 1 L(r, 0, 6; 1, 0, 0) = ¸m[r² + r²ġ² + r² (sin 0)² ¿²] – V(r) . Write down the momenta conjugate to each generalised coordinate. Write down the Hamiltonian and Hamil- ton's equations.
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