Lagrangian Mechanics 04: The Lagrangian of a conservative system in Mechanics

Описание: In this video we demonstrate how one can obtain the form of the Lagrangian of a non-relativistic particle under a conservative force in Classical Mechanics. For our purpose we have demanded that the general definition of momentum of a mechanical system in terms of its Lagrangian should match the Newtonian definition of momentum. This gives the velocity dependence of the Lagrangian. Also using the general definition of momentum and the form of the Lagrange’s equation, along with the definition of a conservative force in Newtonian mechanics we can determine how the Lagrangian should depend on the position coordinates. We further discuss how the form of the Lagrangian thus obtained reveals some general features that Lagrangian of any mechanical system should have.

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Chapters:
0:00 Intro:
1:47 Velocity dependence of the Lagrangian
3:55 The free particle Lagrangian
4:13 Position dependence of the Lagrangian
6:05 Time-dependence of the Lagrangian
7:15 Closed and Open Systems
8:03 General features of the Lagrangian


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Previous videos on Lagrangian Mechanics:
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Lagrangian Mechanics 01: The Action Functional and Action Principle in Physics
   • Lagrangian Mechanics 01: Least Action Prin...  

Lagrangian Mechanics 02: Lagrange's equation from the action principle
   • Lagrangian Mechanics 02: Lagrange's equati...  

Lagrangian Mechanics 03: Energy & Momentum - Links to Conservation laws & symmetry
   • Lagrangian Mechanics 03: Energy & Momentum...  




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Special Relativity videos:
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Observer's world-line is his time axis in a spacetime diagram| Special Relativity
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Lorentz Transformation equations derived from the spacetime diagram
   • Lorentz Transformation equations from the ...  


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