In my text of classical mechanics, it reads: for all relations(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(q_1, q_2, \cdots; \dot{q}_1, \dot{q}_2, \cdots, t) = const.[/tex]

are called first integrals. This definition is very vague. I wonder if it means

1) Any quantities which are not changing with time are called "first integrals" ?

2) If a generalized coordinate is cyclic in Lagrangian equations, can I say this coordinate is one of the first integrals?

3) If the Hamiltonian is not time-dependent explicitly, can I said the energy is one of the first integrals?

What is the general procedure to find all first integrals?

BTW, if there is so called *first* integrals, so is there *second*-integrals?

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# The first integrals

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