Learn · Classical Motion of a Single Particle
Lecture 50 of 58Week 11
Lecture 50: Concept of Phase Space
Prof. Supratik Banerjee · IIT Kanpur
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All the lectures
- Lecture 1: Introduction and Newton's laws of motion
- Lecture 2: From dynamics to Kinematics
- Lecture 3: Equations of dynamics and constants of motion
- Lecture 4: Constants of motion (contd.), Wrok-energy theorem and conservative forces
- Lecture 5: Dynamics under constants and central forces
- Lecture 6: Derivation of gradient form from zero curl condition
- Lecture 7: Concept of equilibrium
- Lecture 8: Terminal velocity, stable and unstable equilibria
- Lecture 9: Stable and unstable equilibria in more than one dimensions
- Lecture 10: Motion in one-dimensional potential
- Lecture 11: Solving equations of motion in one dimension
- Lecture 12: Calculation of Work Done in a Force Field
- Lecture 13: Central forces, Velocity and Acceleration in Plane Polar Coordinates
- Lecture 14: Dynamics and Trajectories Under a Central Force
- Lecture 15: Equation For Trajectories Under a Central Force (contd.): Binet Equation
- Lecture 16: Trajectory of a Particle Under Attractive Inverse-Square Force Law
- Lecture 17: Energy Diagram in an Effective One-Dimensional Motion
- Lecture 18: Two Interesting Problems On the motion Under Central Forces
- Lecture 19: Motion Under an Attractive Inverse-Square Force
- Lecture 20: Motion Under an Attractive Inverse-Square Force (contd.)
- Lecture 21: Trajectories Under Attractive Inverse-Square Force, Laws of Kepler
- Lecture 22: Laplace Runge-Lenz Vector
- Lecture 23: Simple Harmonic Oscillators
- Lecture 24: Two examples of simple harmonic oscillation
- Lecture 25: Forced harmonic oscillator
- Lecture 26: Forced harmonic oscillator at resonance
- Lecture 27: Damped harmonic oscillator
- Lecture 28: Nature of motion under a harmonic potential
- Lecture 29: Comparison among three types of damped oscillation
- Lecture 30: Forced harmonic oscillator with damping
- Lecture 31: A problem on damped harmonic oscillator
- Lecture 32: Beats
- Lecture 33: Motion of a particle in electric and magnetic fields
- Lecture 34: E X B drift
- Lecture 35: Inertial frames of reference, Galilean transformation
- Lecture 36: Non-inertial frames of reference, pseudo forces
- Lecture 37: Motion of a particle in a rotating frame of reference
- Lecture 38: Motion of a particle relative to an observer on earth
- Lecture 39: Motion of a particle under various constraints
- Lecture 40: Principle of Virtual work, D'Alembert's principle
- Lecture 41: Lagrange's equation of first kind
- Lecture 42: Solving problems using Lagrange's equation of first kind
- Lecture 43: Generalized Coordinates and Generalized Velocities
- Lecture 44: Knetic Energy and Acceleration in Terms of Generalized Coordinates
- Lecture 45: Generalized Momentum and Generalized Force; Derivation of Euler-Lagrange Equation
- Lecture 46: Euler Lagrange Equation, Cyclic Coordinates and Other Properties
- Lecture 47: Properties of Euler-Lagrange equations (contd.)
- Lecture 48: Lagrangian of various oscillating systems
- Lecture 49: Problem solving using Euler-Lagrange equations
- Lecture 50: Concept of Phase Space
- Lecture 51: Phase space trajectories and fixed points
- Lecture 52 : Stability of fixed points
- Lecture 53: Different types of fixed points
- Lecture 54: Fixed points and their stability for mechanical systems
- Lecture 55: Linear two-dimensional phase space dynamics
- Lecture 56: Linear two-dimensional phase space dynamics (contd.)
- Lecture 57: Concept of limit cycles
- Lecture 58: Lorenz equations and introduction to chaos