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Thursday, April 19

A brief discussion on classical mechanics Part-02

19 April Physics , 1 Comments

Detailed Topics

1) Constraints of Motion

2) Definition of constraints

3) Examples of constraints of motion

4) Types of constraints of motion
  • Harmonic constraints
  • Non-Harmonic constraints
5) Generalized coordinates

6) Generalized coordinates of some systems
  • Linear harmonic oscillator 
  • Simple pendulum
  • Double pendulum
  • Compound pendulum
  • Spherical pendulum
7) Lagrangian formulation

8) Lagrangian function

9) Lagrangian equation of motion

10) Generalized momentum or canonical momentum

11) Cyclic generalized coordinate




Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

12) Importance of Cyclic generalized coordinate
       a) Body moving under central force

13) Lagrangian function and equation of motion of simple pendulum

14) Lagrangian function and equation of motion of linear harmonic oscillator

15) Conservation of energy by Lagrangian formulation


Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle


16) At wood machine

 17) Hamiltonian function

 18) Hamiltonian equation of motion

 19) Physical significance of Hamiltonian function

 20) Hamiltonian Principle
Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Online Best Notes, Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

Online Best Notes,Detailed Topics 1) Constraints of Motion 2) Definition of constraints 3) Examples of constraints of motion 4) Types of constraints of motion Harmonic constraints Non-Harmonic constraints 5) Generalized coordinates 6) Generalized coordinates of some systems Linear harmonic oscillator Simple pendulum Double pendulum Compound pendulum Spherical pendulum 7) Lagrangian formulation 8) Lagrangian function 9) Lagrangian equation of motion 10) Generalized momentum or canonical momentum 11) Cyclic generalized coordinate 12) Importance of Cyclic generalized coordinate a) Body moving under central force 13) Lagrangian function and equation of motion of simple pendulum 14) Lagrangian function and equation of motion of linear harmonic oscillator 15) Conservation of energy by Lagrangian formulation 16) At wood machine 17) Hamiltonian function 18) Hamiltonian equation of motion 19) Physical significance of Hamiltonian function 20) Hamiltonian Principle

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