An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentzlike gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit. PACS numbers: 45.20.D-, 91.10.Sp, 04.25.Nx 1.

We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultra-stationary metrics to exact magnetic tidal tensors of electromagnetism in curved spaces. In the third we show that our approach leads to two-step exact derivation of the Papapetrou force on a gyroscope. We then establish a new proof for a class of tensor identities that define invariants of the type E 2 − B 2 and E · B, and we exhibit the invariants built from tidal tensors in both gravity and electromagnetism. We contrast our approach with the two gravito-electromagnetic analogies commonly found in the literature, and argue that it sheds light on the debate about the limit of validity of one of the analogies, and clarifies issues concerning the physical interpretation of the other.

The need to know the force exerted by moving body on ground of intriguing interplay between geometry and dynamics gives a possible introducing of gravitomagnetic (GM) field as an analogous to the magnetic field. The existence of such a field has straightforwardly been presented in two approaches based on special relativity (SR) only and SR plus gravitational time dilation (semi SR) for different cases. We treat these two approaches for when the cases are switched, using appropriate key points. Hence, we demonstrate that the strength of GM field in semi SR approach is twice SR approach. Then, we also discuss that the full linearized general relativity should give the same strength for GM field as semi SR, and hence, through an exact analogy with the electrodynamic equations, we present an argument for the best potential definition amongst those used in this issue. PACS number: 03.30. + p; 04.20. − q