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Course11510453558 lectures

Classical Motion of a Single Particle

Prof. Supratik Banerjee · IIT Kanpur

Start with lecture 1 At NPTEL

About

This undergraduate level course is designed to offer a systematic development of the basic concepts of classical mechanics of a single particle. A special emphasis will be given on the vector formulation of the problems of dynamics which are appropriate for understanding and analyzing the motion of a particle in more than one dimensions. The notion of symmetry and conservation and their importance in classical dynamics will be discussed to pave the way for the motivated students to advance theories of physics. A separate section will be dedicated introducing the generalized coordinates, generalized velocities and the method of Lagrangian to solve constrained motions of a single particle. Finally, the phase space dynamics along with some introductory elements of nonlinear dynamics related to the motion of a single particle will be discussed.

Intended audience: 1st and 2nd year UG students and anyone interested in understanding the basics of classical mechanics

Prerequisites: Basics knowledge of calculus, partial differentiation and vector algebra is preferred

Lectures

Week 01

  1. Lecture 1: Introduction and Newton's laws of motion YouTube
  2. Lecture 2: From dynamics to Kinematics YouTube
  3. Lecture 3: Equations of dynamics and constants of motion YouTube
  4. Lecture 4: Constants of motion (contd.), Wrok-energy theorem and conservative forces YouTube
  5. Lecture 5: Dynamics under constants and central forces YouTube

Week 02

  1. Lecture 6: Derivation of gradient form from zero curl condition YouTube
  2. Lecture 7: Concept of equilibrium YouTube
  3. Lecture 8: Terminal velocity, stable and unstable equilibria YouTube
  4. Lecture 9: Stable and unstable equilibria in more than one dimensions YouTube
  5. Lecture 10: Motion in one-dimensional potential YouTube
  6. Lecture 11: Solving equations of motion in one dimension YouTube

Week 03

  1. Lecture 12: Calculation of Work Done in a Force Field YouTube
  2. Lecture 13: Central forces, Velocity and Acceleration in Plane Polar Coordinates YouTube
  3. Lecture 14: Dynamics and Trajectories Under a Central Force YouTube
  4. Lecture 15: Equation For Trajectories Under a Central Force (contd.): Binet Equation YouTube
  5. Lecture 16: Trajectory of a Particle Under Attractive Inverse-Square Force Law YouTube

Week 04

  1. Lecture 17: Energy Diagram in an Effective One-Dimensional Motion YouTube
  2. Lecture 18: Two Interesting Problems On the motion Under Central Forces YouTube
  3. Lecture 19: Motion Under an Attractive Inverse-Square Force YouTube
  4. Lecture 20: Motion Under an Attractive Inverse-Square Force (contd.) YouTube
  5. Lecture 21: Trajectories Under Attractive Inverse-Square Force, Laws of Kepler YouTube
  6. Lecture 22: Laplace Runge-Lenz Vector YouTube

Week 05

  1. Lecture 23: Simple Harmonic Oscillators YouTube
  2. Lecture 24: Two examples of simple harmonic oscillation YouTube
  3. Lecture 25: Forced harmonic oscillator YouTube
  4. Lecture 26: Forced harmonic oscillator at resonance YouTube
  5. Lecture 27: Damped harmonic oscillator YouTube
  6. Lecture 28: Nature of motion under a harmonic potential YouTube

Week 06

  1. Lecture 29: Comparison among three types of damped oscillation YouTube
  2. Lecture 30: Forced harmonic oscillator with damping YouTube
  3. Lecture 31: A problem on damped harmonic oscillator YouTube
  4. Lecture 32: Beats YouTube
  5. Lecture 33: Motion of a particle in electric and magnetic fields YouTube
  6. Lecture 34: E X B drift YouTube

Week 07

  1. Lecture 35: Inertial frames of reference, Galilean transformation YouTube
  2. Lecture 36: Non-inertial frames of reference, pseudo forces YouTube
  3. Lecture 37: Motion of a particle in a rotating frame of reference YouTube
  4. Lecture 38: Motion of a particle relative to an observer on earth YouTube

Week 08

  1. Lecture 39: Motion of a particle under various constraints YouTube
  2. Lecture 40: Principle of Virtual work, D'Alembert's principle YouTube
  3. Lecture 41: Lagrange's equation of first kind YouTube
  4. Lecture 42: Solving problems using Lagrange's equation of first kind YouTube

Week 09

  1. Lecture 43: Generalized Coordinates and Generalized Velocities YouTube
  2. Lecture 44: Knetic Energy and Acceleration in Terms of Generalized Coordinates YouTube
  3. Lecture 45: Generalized Momentum and Generalized Force; Derivation of Euler-Lagrange Equation YouTube
  4. Lecture 46: Euler Lagrange Equation, Cyclic Coordinates and Other Properties YouTube

Week 10

  1. Lecture 47: Properties of Euler-Lagrange equations (contd.) YouTube
  2. Lecture 48: Lagrangian of various oscillating systems YouTube
  3. Lecture 49: Problem solving using Euler-Lagrange equations YouTube

Week 11

  1. Lecture 50: Concept of Phase Space YouTube
  2. Lecture 51: Phase space trajectories and fixed points YouTube
  3. Lecture 52 : Stability of fixed points YouTube
  4. Lecture 53: Different types of fixed points YouTube
  5. Lecture 54: Fixed points and their stability for mechanical systems YouTube

Week 12

  1. Lecture 55: Linear two-dimensional phase space dynamics YouTube
  2. Lecture 56: Linear two-dimensional phase space dynamics (contd.) YouTube
  3. Lecture 57: Concept of limit cycles YouTube
  4. Lecture 58: Lorenz equations and introduction to chaos YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Physics
Teacher
Prof. Supratik Banerjee
Level
Undergraduate
Language
English
Subjects
Physics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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