In Landau's Mechanics it is written that there are some integrals of the motion deriving from the fundamental homogeneity and isotropy of space and time. Momentum is related to the homogeneity of space; energy to the homogeneity of time; angular momentum to the isotropy of space. Which is the integral deriving from the isotropy of time?
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Qmechanic
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Paolo Secchi
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2What do you mean by "istropy of time"? How do you rotate time? – mike stone Feb 06 '22 at 18:13
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It means that replacing $t$ with $-t$ the Lagrangian is unchanged and thus the laws of classical mechanics are reversible. – Paolo Secchi Feb 06 '22 at 18:19
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3$t\to -t$ is not a continuous transformation. Constants of the motion arise from continuous transformations, not discrete ones. – mike stone Feb 06 '22 at 18:26
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Possible duplicate: https://physics.stackexchange.com/q/185264/2451 – Qmechanic Feb 06 '22 at 19:06