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Problem with symmetry and integral of motion in Classical Mechanics [closed]
I am currently working through the problem 4.10 in Kotkin and Serbo's book "Collection of Problems in Classical Mechanics". The problem consists in showing that the quantity
\begin{equation}
...
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4
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Quantity conserved for the 3D spherically symmetric harmonic potential $V(r)=\alpha r^2$ [duplicate]
I know that in the case of the Kepler problem there is a quantity (other than energy, momentum,...) conserved which is the Runge-Lenz vector.
Is there also an "exotic" quantity conserved for a 2-Body ...
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26
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Constants of motion vs. integrals of motion vs. first integrals
Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
user17116
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Do symmetries increase the number of conserved quantities? [closed]
Let us consider a classical mechanical system of N particles in a constant external field. We have 3N coordinates and 3N velocities, so totally 6N unknown variables. We have 6N ordinary differential ...
