A learn's puzzle on transformation equation

[atreess]

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?

 

[gabbagabbahey]

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?

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

For example, consider a particle in 1-D motion described by $x(t)=v_0t$. There is no reason you can't define a new variable $q(x,t)=3x+a_0 t^2$, if you have some use for that transformation.

 

[atreess]

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.

 

[atreess]

I guess that t represents the change of the constraint with time. Is it right?