Sunday, September 15, 2019

classical mechanics - Uniqueness of the number of degrees of freedom


As per my knowledge, degrees of freedom of any physical system are the number of independent quantities(coordinates) which need to be specified in order to specify the state of a system uniquely. However, my question is, why is there a unique number of degrees of freedom for any system?


Or, to put it differently, if a set of $n$ independent coordinates describes the state of the system completely, why is it true that any other set of $n$ independent coordinates also describes the state of the system completely?


And why can there not be a set of $m$ independent coordinated which also describe the state of the system completely, where $m>n$ ?





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