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A learn's puzzle on transformation equation

  1. Aug 24, 2010 #1
    Hi, I'm a new learner of CM and I was stuck at the very beginning. TT
    The transformation equation is ri=ri(q1,q2,...,qn,t)
    I wonder why t should be in the bracket.
    Aren't r determined by these independent coordinates? Isn't t already contained in them?
     
    Last edited: Aug 24, 2010
  2. jcsd
  3. Aug 24, 2010 #2

    gabbagabbahey

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    Certainly the [itex]q_{i}[/itex] can have some time-dependence, and that gives [itex]r_{i}[/itex] implicit time-dependence. But, you can also choose to define some new coordinates [itex]r_{i}[/itex] with explicit dependence on time.

    For example, consider a particle in 1-D motion described by [itex]x(t)=v_0t[/itex]. There is no reason you can't define a new variable [itex]q(x,t)=3x+a_0 t^2[/itex], if you have some use for that transformation.
     
  4. Aug 25, 2010 #3
    Thanks very much for your reply!
    But how about the degrees of freedom? A system with n degrees of freedom just needs n independent coordinates. If adding t, there must be one coordinate(q1, q2,..., or t) which is dependent. :confused:
     
  5. Aug 31, 2010 #4
    I guess that t represents the change of the constraint with time. Is it right?
     
    Last edited: Aug 31, 2010
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