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 | ||
Course Reviews
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