Lagrangian and equation of motion

vivitribal
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In general how do you demonstrate that a given Lagrangian equation provides the correct equation of motion?
 
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By computing the equations of motion ? :rolleyes:

Daniel.
 
The whole point of using the Lagrangian is that any physically possible motion must make the Lagrangian (Kinetic energy minus potential energy) an extremum. Apply "calculus of variations" (essentially the Euler-Lagrange equation) to the Lagrangian to derive the equations of motion.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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