A particle of mass m moves in a constant field of attractive force a/r² e−ᵇᵗ. Find the Lagrangian and Hamiltonian.
A. Lagrangian: L= 1/2 m (ṙ²+r²θ²+r²sin²θϕ²) + a/r e−ᵇᵗ, Hamiltonian: H= 1/2m (²pᵣ+²p_θ/r²+²p_ϕ/r²sin²θ) - a/r e−ᵇᵗ
B. Lagrangian: L= 1/2 m (ṙ²+r²θ²+r²sin²θϕ²) - a/r e−ᵇᵗ, Hamiltonian: H= 1/2m (²pᵣ+²p_θ/r²+²p_ϕ/r²sin²θ) + a/r e−ᵇᵗ
C. Lagrangian: L= 1/2 m (ṙ²+r²θ²+r²sin²θϕ²) + a/r e−ᵇᵗ, Hamiltonian: H= 1/2m (²pᵣ+²p_θ/r²+²p_ϕ/r²sin²θ) - a/r e−ᵇᵗ
D. Lagrangian: L= 1/2 m (ṙ²+r²θ²+r²sin²θϕ²) - a/r e−ᵇᵗ, Hamiltonian: H= 1/2m (²pᵣ+²p_θ/r²+²p_ϕ/r²sin²θ) + a/r e−ᵇᵗ
