GATE Classical Mechanics: Hamiltonian and Hamilton's equations of motion – Previous Year Questions

5 GATE previous year questions on Hamiltonian and Hamilton's equations of motion (Classical Mechanics, Physics) with answers and explanations, from every paper.

1. GATE 2023 PH Q42 (2 marks, Multiple choice) – A particle moves on a frictionless horizontal (r,) plane under F=-k r/(2r3). For conjugate momenta p r,p , what is dp r/dt?
2. GATE 2025 PH Q51 (2 marks, Multiple select) – A particle of mass m and charge q in uniform magnetic field 2B z has L= m2v2+qB(xv y-yv x). With conjugate momenta p x,p y,p z and Hamiltonian H,…
3. GATE 2025 PH Q52 (2 marks, Multiple select) – A bead is constrained to move along a long, massless, frictionless horizontal rod parallel to the x axis. The rod itself is moving vertically upward…
4. GATE 2025 PH Q62 (2 marks, Numerical answer) – The Hamiltonian is H(p,q)=p2/(2m)+q2A(q) with real A(q). If m q=-5qA(q) and dA/dq=nA(q)/q, the value of n (in integer) is
5. GATE 2024 PH Q38 (2 marks, Multiple choice) – For L=m x y-m 02xy with conjugate momenta p x,p y, the canonical equations are