Note 361(1): General Dynamics with the Lagrange Derivative

The acceleration in general is defined by the complete convective or Lagrange derivative of velocity (Eq.(1)). This is shown to be a Cartan covariant derivative in which the spin connection matrix is the Jacobian, Eq. (9). The non Newtonian acceleration is defined by the Lagrange derivative (14). By choice of solution (16), the non Newtonian acceleration can be reduced to an inverse square law for any coordinate system. Without the non Newtonian acceleration the orbit cannot be defined. Due to ECE2 unification of gravitation, dynamics and fluid dynamics, the orbital force equation becomes the Euler equation (33) of fluid dynamics. In the next note it will be shown that the general non Newtonian acceleration reduces to that derived in plane polar coordinates by choice of coordinate system. So the dynamics and coordinate system become the same concept of general relativity. In general this method gives new accelerations which should be looked for in astronomy.


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