- #1

Kashmir

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A system has some holonomic constraints. Using them we can have a set of coordinates ##{q_i}##. Since any values for these coordinates is possible we say that these are independent coordinates.

However the system will trace a path in the configuration space ,which means that actually all our independent coordinates are in fact dependent.

Why do we then say that we have independent coordinates?

For example,

Goldstein

>The fundamental problem of the calculus of variations is easily generalized to the case where ##f## is a function of many **independent variables** ##y_{i}##, and their derivatives ##\dot{y}_{i}##. (Of course, all these quantities are considered as functions of the parametric variable ##x##.) Then a variation of the integral ##J##,

##

\delta J=\delta \int_{1}^{2} f\left(y_{1}(x) ; y_{2}(x), \ldots, \dot{y}_{1}(x) ; \dot{y}_{2}(x), \ldots, x\right) d x

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