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Basic Intro Course for Physics (AI Based) , DoAS (MIRRC)
·
Module 3
Analytical Mechanics
1
Calculus of Variations and the Brachistochrone Problem
Apply the calculus of variations to find functions that extremize functionals, such as finding the brachistochrone.
2
Euler-Lagrange Equation from Hamilton's Principle
Derive the Euler-Lagrange equation from the Principle of Least Action (Hamilton's Principle).
3
Lagrangian Formulation with Generalized Coordinates
Formulate the Lagrangian for mechanical systems using generalized coordinates.
4
Solving Mechanics Problems with Euler-Lagrange Equations
Solve constrained and unconstrained mechanics problems using the Euler-Lagrange equations.
5
Cyclic Coordinates and Noether's Theorem
Identify cyclic (ignorable) coordinates and apply Noether's theorem to find conserved quantities.
6
From Lagrangian to Hamiltonian: Deriving Hamilton's Equations
Perform the Legendre transformation to derive Hamilton's equations from the Lagrangian.
7
Hamiltonian Mechanics: Problem Solving
Solve mechanics problems using Hamiltonian formalism.
8
Phase Space Diagrams for Hamiltonian Systems
Construct and interpret phase space diagrams for simple Hamiltonian systems.
Previous module
Rotational Dynamics and Oscillations
Next module
Mathematical Methods for Physics