Physics Optional PYQ solution - Topic Wise

Mechanics; Waves & Optics; Electricity & Magnetism; Thermal & Statistical Physics; Quantum Mechanics; Atomic & Molecular Physics; Nuclear & Particle Physics ; Solid state physics & electronics.

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Lagrangian & Hamiltonian Mechanics

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This is a standard derivation frequently asked in UPSC Physics Optional. The key is to set up the formalism correctly before computing.

Lagrangian: L = T − V | Euler-Lagrange: d/dt(∂L/∂q̇) − ∂L/∂q = 0

Step-by-step solution:

Define the system and identify generalised coordinates q₁, q₂, …
Write expressions for kinetic energy T and potential energy V.
Form the Lagrangian L = T − V.
Apply the Euler-Lagrange equation to each coordinate.
Simplify to obtain the equations of motion. Identify conserved quantities from cyclic coordinates.

📐 Diagram: Phase portrait / free body diagram would be drawn here in the actual answer sheet. Always include a neat diagram in UPSC answers.

UPSC Tip: For a 15-mark question, spend the first 2 minutes planning your answer structure: definition → derivation → result → significance/application.

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