# Classical Motion of a Single Particle

- Institution: IIT Kanpur
- Department: Physics
- Teacher: Prof. Supratik Banerjee
- Level: Undergraduate
- Language: English
- Subjects: Physics
- Source: [NPTEL](https://nptel.ac.in/courses/115104535)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/115104535)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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

1. [Lecture 1: Introduction and Newton's laws of motion](https://invisiblenetwork.ai/learn/nptel/115104535/3621141be809) (YouTube)
2. [Lecture 2: From dynamics to Kinematics](https://invisiblenetwork.ai/learn/nptel/115104535/71c232836b17) (YouTube)
3. [Lecture 3: Equations of dynamics and constants of motion](https://invisiblenetwork.ai/learn/nptel/115104535/af3c59288c3f) (YouTube)
4. [Lecture 4: Constants of motion (contd.), Wrok-energy theorem and conservative forces](https://invisiblenetwork.ai/learn/nptel/115104535/4f838932df66) (YouTube)
5. [Lecture 5: Dynamics under constants and central forces](https://invisiblenetwork.ai/learn/nptel/115104535/0469a4184d68) (YouTube)
6. [Lecture 6: Derivation of gradient form from zero curl condition](https://invisiblenetwork.ai/learn/nptel/115104535/49d2c14c71cd) (YouTube)
7. [Lecture 7: Concept of equilibrium](https://invisiblenetwork.ai/learn/nptel/115104535/51b9e7e615a1) (YouTube)
8. [Lecture 8: Terminal velocity, stable and unstable equilibria](https://invisiblenetwork.ai/learn/nptel/115104535/e2e5957ed949) (YouTube)
9. [Lecture 9: Stable and unstable equilibria in more than one dimensions](https://invisiblenetwork.ai/learn/nptel/115104535/1995e77efee4) (YouTube)
10. [Lecture 10: Motion in one-dimensional potential](https://invisiblenetwork.ai/learn/nptel/115104535/5a556d60ba0e) (YouTube)
11. [Lecture 11: Solving equations of motion in one dimension](https://invisiblenetwork.ai/learn/nptel/115104535/05906b237422) (YouTube)
12. [Lecture 12: Calculation of Work Done in a Force Field](https://invisiblenetwork.ai/learn/nptel/115104535/4bc65dc7555d) (YouTube)
13. [Lecture 13: Central forces, Velocity and Acceleration in Plane Polar Coordinates](https://invisiblenetwork.ai/learn/nptel/115104535/a19d8f35ddb1) (YouTube)
14. [Lecture 14: Dynamics and Trajectories Under a Central Force](https://invisiblenetwork.ai/learn/nptel/115104535/23672b5960f5) (YouTube)
15. [Lecture 15: Equation For Trajectories Under a Central Force (contd.): Binet Equation](https://invisiblenetwork.ai/learn/nptel/115104535/2bb60cd97396) (YouTube)
16. [Lecture 16: Trajectory of a Particle Under Attractive Inverse-Square Force Law](https://invisiblenetwork.ai/learn/nptel/115104535/d201c914d1ec) (YouTube)
17. [Lecture 17: Energy Diagram in an Effective One-Dimensional Motion](https://invisiblenetwork.ai/learn/nptel/115104535/a308a0ca6e6a) (YouTube)
18. [Lecture 18: Two Interesting Problems On the motion Under Central Forces](https://invisiblenetwork.ai/learn/nptel/115104535/3831cef72896) (YouTube)
19. [Lecture 19: Motion Under an Attractive Inverse-Square Force](https://invisiblenetwork.ai/learn/nptel/115104535/fbcfdc418f72) (YouTube)
20. [Lecture 20: Motion Under an Attractive Inverse-Square Force (contd.)](https://invisiblenetwork.ai/learn/nptel/115104535/7f4d01d1f941) (YouTube)
21. [Lecture 21: Trajectories Under Attractive Inverse-Square Force, Laws of Kepler](https://invisiblenetwork.ai/learn/nptel/115104535/56ee74f2983e) (YouTube)
22. [Lecture 22: Laplace Runge-Lenz Vector](https://invisiblenetwork.ai/learn/nptel/115104535/3c91f74b0520) (YouTube)
23. [Lecture 23: Simple Harmonic Oscillators](https://invisiblenetwork.ai/learn/nptel/115104535/5905fd793982) (YouTube)
24. [Lecture 24: Two examples of simple harmonic oscillation](https://invisiblenetwork.ai/learn/nptel/115104535/9e8cc97a51d8) (YouTube)
25. [Lecture 25: Forced harmonic oscillator](https://invisiblenetwork.ai/learn/nptel/115104535/99222bf674aa) (YouTube)
26. [Lecture 26: Forced harmonic oscillator at resonance](https://invisiblenetwork.ai/learn/nptel/115104535/fe198cbc36aa) (YouTube)
27. [Lecture 27: Damped harmonic oscillator](https://invisiblenetwork.ai/learn/nptel/115104535/f9b84d9f7eec) (YouTube)
28. [Lecture 28: Nature of motion under a harmonic potential](https://invisiblenetwork.ai/learn/nptel/115104535/48fa320b7e14) (YouTube)
29. [Lecture 29: Comparison among three types of damped oscillation](https://invisiblenetwork.ai/learn/nptel/115104535/e47327a296e3) (YouTube)
30. [Lecture 30: Forced harmonic oscillator with damping](https://invisiblenetwork.ai/learn/nptel/115104535/f39e24d88140) (YouTube)
31. [Lecture 31: A problem on damped harmonic oscillator](https://invisiblenetwork.ai/learn/nptel/115104535/b6522e9343af) (YouTube)
32. [Lecture 32: Beats](https://invisiblenetwork.ai/learn/nptel/115104535/bba2b94b5a37) (YouTube)
33. [Lecture 33: Motion of a particle in electric and magnetic fields](https://invisiblenetwork.ai/learn/nptel/115104535/57981d14e0b1) (YouTube)
34. [Lecture 34: E X B drift](https://invisiblenetwork.ai/learn/nptel/115104535/6e19b53fc29a) (YouTube)
35. [Lecture 35: Inertial frames of reference, Galilean transformation](https://invisiblenetwork.ai/learn/nptel/115104535/03ee3664f229) (YouTube)
36. [Lecture 36: Non-inertial frames of reference, pseudo forces](https://invisiblenetwork.ai/learn/nptel/115104535/f45b780c1a6a) (YouTube)
37. [Lecture 37: Motion of a particle in a rotating frame of reference](https://invisiblenetwork.ai/learn/nptel/115104535/cc7b3651e521) (YouTube)
38. [Lecture 38: Motion of a particle relative to an observer on earth](https://invisiblenetwork.ai/learn/nptel/115104535/1d44f7dc3af9) (YouTube)
39. [Lecture 39: Motion of a particle under various constraints](https://invisiblenetwork.ai/learn/nptel/115104535/8854463e69f8) (YouTube)
40. [Lecture 40: Principle of Virtual work, D'Alembert's principle](https://invisiblenetwork.ai/learn/nptel/115104535/63d217c03238) (YouTube)
41. [Lecture 41: Lagrange's equation of first kind](https://invisiblenetwork.ai/learn/nptel/115104535/e80ef45749c7) (YouTube)
42. [Lecture 42: Solving problems using Lagrange's equation of first kind](https://invisiblenetwork.ai/learn/nptel/115104535/937d1c419ef2) (YouTube)
43. [Lecture 43: Generalized Coordinates and Generalized Velocities](https://invisiblenetwork.ai/learn/nptel/115104535/e8c3747081d1) (YouTube)
44. [Lecture 44: Knetic Energy and Acceleration in Terms of Generalized Coordinates](https://invisiblenetwork.ai/learn/nptel/115104535/a25f06fc626c) (YouTube)
45. [Lecture 45: Generalized Momentum and Generalized Force; Derivation of Euler-Lagrange Equation](https://invisiblenetwork.ai/learn/nptel/115104535/f7346a2f3a87) (YouTube)
46. [Lecture 46: Euler Lagrange Equation, Cyclic Coordinates and Other Properties](https://invisiblenetwork.ai/learn/nptel/115104535/41bb9ef69aea) (YouTube)
47. [Lecture 47: Properties of Euler-Lagrange equations (contd.)](https://invisiblenetwork.ai/learn/nptel/115104535/446bbd281f6c) (YouTube)
48. [Lecture 48: Lagrangian of various oscillating systems](https://invisiblenetwork.ai/learn/nptel/115104535/5670affa4f50) (YouTube)
49. [Lecture 49: Problem solving using Euler-Lagrange equations](https://invisiblenetwork.ai/learn/nptel/115104535/d9fc709bfab5) (YouTube)
50. [Lecture 50: Concept of Phase Space](https://invisiblenetwork.ai/learn/nptel/115104535/5064f313e006) (YouTube)
51. [Lecture 51: Phase space trajectories and fixed points](https://invisiblenetwork.ai/learn/nptel/115104535/4a4202d3845c) (YouTube)
52. [Lecture 52 : Stability of fixed points](https://invisiblenetwork.ai/learn/nptel/115104535/435a6bf85598) (YouTube)
53. [Lecture 53: Different types of fixed points](https://invisiblenetwork.ai/learn/nptel/115104535/9c6553563123) (YouTube)
54. [Lecture 54: Fixed points and their stability for mechanical systems](https://invisiblenetwork.ai/learn/nptel/115104535/be17da54199c) (YouTube)
55. [Lecture 55: Linear two-dimensional phase space dynamics](https://invisiblenetwork.ai/learn/nptel/115104535/dfbe35093a65) (YouTube)
56. [Lecture 56: Linear two-dimensional phase space dynamics (contd.)](https://invisiblenetwork.ai/learn/nptel/115104535/ef37d5c32c51) (YouTube)
57. [Lecture 57: Concept of limit cycles](https://invisiblenetwork.ai/learn/nptel/115104535/74f8241c133f) (YouTube)
58. [Lecture 58: Lorenz equations and introduction to chaos](https://invisiblenetwork.ai/learn/nptel/115104535/32888fa308ff) (YouTube)