According to Hamilton's equation....the relation $$ 2T = \sum_ip_i\dot q_i $$ is obvious. But How would I show that kinetic energy is homogeneous quadratic function of generalised velocities $\dot q_i$?
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Please use LaTeX to format mathematical symbols and formulas. Here is a link to a quick tutorial: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – edm Oct 28 '18 at 08:53
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Please edit and expand your question. To properly compose formulas that are then displayed with correct formatting, see mathjax basic tutorial, a discussion of additional resources can be found here. Please add more context to your question, it is no clear what you are asking specifically. For the general topic, consult a textbook on Hamilton mechanics, Arnol'd is nice if somewhat advanced,... – Lutz Lehmann Oct 28 '18 at 08:54
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This is a very good question in physics stack exchange – Fakemistake Oct 28 '18 at 08:59