The latest note gives a rigorously self consistent solution with conservation of relativistic angular momentum. Marion and Thornton define a beta = v / c which is used throughout chapter fourteen of teh third edition. I can give a few examples of how this beta should be used. The Lorentz boost in different directions is also discussed by Carroll and Ryder, and also in "The Enbigmatic Photon" (online in the Omnia Opera). In their lagrangian in Eq. (14.111) there are components u sub i and also beta. I can write a note to clarify how beta should be used.
Date: Thu, Feb 22, 2018 at 8:38 AM
Subject: Re: 402(3): The Generalized Momentum
To: Myron Evans <myronevans123>
There seems to be an intricate point with the gamma factor: according to eq.(11) of the note, gamma contains the velocity component v_i for each generalized coordinate q_i. This is different from using the modulus of v in all component equations.
Horst
Am 19.02.2018 um 15:44 schrieb Myron Evans:
This Eq. (6.151) of Marion and Thornton, third edition. the term as introduced in Kelvin and Tait, "Natural Philosophy" (1867). It is the origin of the Lagrange equations of motion, and also the origin of the relativistic lagrangian. The relativistic momentum as used by Einstein is derived from the conservation of momentum. Horst has found that the relativistic Newtonian force, the time derivative of the relativistic momentum, gives retrograde precession, a major discovery because EGR fails to give retrograde precession.