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Newton’s laws. Dynamical systems, Phase space dynamics, stability analysis. Central force motions.Two body Collisions – scattering in laboratory and Centre of mass frames. Rigid body dynamicsmoment of inertia tensor. Non-inertial frames and pseudoforces. Variational principle. Generalizedcoordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativityLorentz transformations, relativistic kinematics and mass–energy equivalence.

Dynamical systems, Phase space dynamics, stability analysis. Poisson brackets and canonical transformations. Symmetry, invariance and Noether’s theorem. Hamilton-Jacobi theory.

 

 

Course Curriculum

PRE-REQUISITES
Normal Reaction FREE 00:36:00
Tension 00:35:00
Pseudo Forces 01:01:00
Friction 00:51:00
Law of Conservation of Linear Momentum 00:47:00
Law of Conservation of Energy 00:39:00
Collision 01:35:00
GENERALISED NOTATION
Generalized Notation 02:16:00
LAGRANGIAN FORMULATION OF MECHANICS
DAlembert Principle and Lagrange Equation 02:01:00
Lagrange Equation from Variational Principle 01:41:00
Problems on Lagrangian FREE 00:54:00
Symmetry and Conservation Laws 01:14:00
JEST and GATE Previous Years Problems on Lagrangian 00:25:00
CSIRNET Previous Years Problems on Lagrangian 00:36:00
HAMILTONIAN FORMULTION OF MECHANICS
Hamiltonian Formulation 00:30:00
Problems on Hamiltonian 00:26:00
JEST Previous Year Problems on Hamiltonian 00:11:00
GATE Previous Year Problems on Hamiltonian 00:40:00
CSIR NET Previous Year Problems on Hamiltonian 00:50:00
CENTRAL FORCES
Equivalent One Body Problem 00:49:00
Conservation laws in Central Force Motion FREE 00:37:00
Trajectory of Particle Undergoing Central Force Motion 00:43:00
Types of Central Force Motion 02:19:00
Problems on Central Forces 01:44:00
Gravitation 00:25:00
Gravitational Field 01:42:00
Gravitational Potential 00:52:00
Gravitational Potential Energy 01:41:00
Collision and Scattering 01:44:00
Previous Year Problems on Central Forces in IISc 00:36:00
Previous Year Problems on Central Forces in TIFR 00:34:00
Previous Year Problems on Central Forces in JEST 01:49:00
GATE Previous Year Problems on Central Forces 00:24:00
CSIR NET Previous Year Problems on Central Forces FREE 01:05:00
UNIFORMLY ROTATING FRAME
Uniformly Rotating Frame 00:57:00
Circular Motion FREE 01:43:00
Coriolis Force 00:27:00
Previous Years Questions on Coriolis forces FREE 00:42:00
SMALL OSCILLATIONS
Small Oscillation in One Dimension 02:27:00
Coupled Oscillation 00:52:00
JEST Previous Year Problems on Small Oscillations 00:14:00
GATE Previous Year Problems on Small Oscillations 00:35:00
CSIR NET Previous Year Problems on Small Oscillations 01:42:00
PHASE SPACE DYNAMICS
First Order System 00:36:00
Second Order System and Stability Analysis 00:45:00
Examples 00:38:00
Previous Year Problems on Phase Space Dynamics 00:26:00
RIGID BODY DYNAMICS
Degree of Freedom and Euler Angles 01:16:00
Rotation about Fixed Axis 01:48:00
Translation + Rotation FREE 01:07:00
Angular Momentum 01:25:00
Moment of Inertia Tensor 00:48:00
Euler Equations and Its Applications 00:35:00
Previous Year Problems on Rigid Body Dynamics in IISc 00:56:00
Previous Year Problems on Rigid Body Dynamics in TIFR 00:46:00
Previous Year Problems on Rigid Body Dynamics in JEST 00:15:00
GATE Previous Years Problems on Rigid Body Dynamics 00:33:00
CSIR NET Previous Years Problems on Rigid Body Dynamics FREE 00:16:00
SPECIAL THEORY OF RELATIVITY
Einstein postulates 00:25:00
Time Dilation and Length Contraction 00:34:00
Simultanity and Lorentz Transformation 00:25:00
Problems on Relativity 00:54:00
Mass and Energy 00:37:00
Minkowsky Space 00:44:00
IISc Previous Year Problems on Relativity 00:41:00
TIFR Previous Year Problems on Relativity 00:36:00
JEST Previous Year Problems on Relativity 00:34:00
GATE Previous Year Problems on Relativity 01:33:00
CSIR NET Previous Year Problems on Relativity 01:02:00
CANONICAL TRANSFORMATION
Canonical Transformation 00:00:00

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