Lagrangian Mechanics

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Lagrangian Mechanics
Lagrangian Mechanics is the reformulation of Newtonian Mechanics that utilizes the Lagrangian defined byL=T-UwhereT= total kinetic energy of a system

of particles
U= sum of the potential energy functions of a system of particlesIn other branches of physics, the Lagrangian is defined as the functionL: TQ–> RWhere Q is the configuration space, a subset of R^3N
such that the action, defined as the functional,A(q)= int(L) dt
when it reaches stationary value at {q(t)}, will male {q(t)} the equations of motion.
Note, int() means the integration notation with the limits of integration being positive an negative infinity, respectively.It is shown, using the Calculus of Variations, that the equations of motion are in such a way that they satisfy the Lagrange’s Equations of motionD(d(L)/dv)-d(L)/dq=0
Where D is the differential operator with respect to time, d/dx stands for partial differentiation, and v is the generalized velocity.

Bob: Why is general relativity so tough to learn?!

Doug: Cause’ you don’t know enough Lagrangian Mechanics!
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