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_{1},q

_{2},...,q

_{n}be generalized coordinates of a holonomic system and T its kinetic energy. q

_{k}correspondes to a translation of the entire system and q

_{j}a rotation of the entire system around some axis, then ∂

_{qj}T=∂

_{qk}T=0 since velocities are not affected by a translation of the origin or a rotation of the coordinate axes.

Now take as an example the kinetic energy of a single particle in spherical coordiantes, here the polar angle θ correspondes to a rotation of the system, but T is dependent on θ. r correspondes to a translation of the particle and therefore the system but T depends on r. How should I undersand this?

Mvh. Frederik