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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F857d1b55-875c-4f26-a9e3-d336b033cff4%2F4e141d5f-707c-4512-ab86-01ffcfc4b64a%2Fb6xiuj_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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