B Exploring Holonomic Basis in Cartesian Coordinates

mairzydoats
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Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?
 
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How do you define cartesian coordinates?
 
martinbn said:
How do you define cartesian coordinates?
I would assume rectangular coordinates with basis ##e_i = \delta _i^j##
 

Thread 'On covariance of the Lagrange equations'

Here is a sketch of deduction of the Lagrange equations by means of the covariance argument. I believe that it is a suitable substitute for the archaic terminology that is employed in most textbooks. Assume we have ##\nu## particles with masses ##m_1,\ldots,m_\nu## and with position vectors $$\boldsymbol r_i=(x^{3(i-1)+1},x^{3(i-1)+2},x^{3(i-1)+3})\in\mathbb{R}^3,\quad i=1,\ldots,\nu.$$ Thus the position of the system is characterized by a vector...
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