Related papers: Third order variational equation for the free rela…
We prove that well known first-order (in spin, momentum, and space-time coordinates) equations of motion of relativistic top are equivalent to the third-order equations of Mathisson on the surface of the Mathisson-Pirani auxiliary…
A variational equation of the fourth order for the free relativistic top is developed starting from the Dixon's system of equations for the motion of the relativistic dipole. The obtained equation is then cast into the homogeneous…
A second order variational description of the autoparallel curves of some differential-geometric connection for the third order Mathisson's 'new mechanics' of a relativistic free spinning particle is suggested starting from general…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
A parameter-invariant variational problem with a manifestly covariant Lagrangian function of second order is considered, which covers the case of the free relativistic top at constraint manifold of constant acceleration
We derive a linearly causal and stable third-order relativistic fluid-dynamical theory from the Boltzmann equation using the method of moments. For this purpose, we demonstrate that such theory must include novel degrees of freedom,…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
Mathisson's 'new mechanics' of a relativistic spinning particle is shown to follow, in the case of planar motion, from only general requirements of relativistic invariance and of the dependence on third order derivatives along with the…
An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve…
We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0\gamma\mathbf{v}$ is…
Using the relativistic quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding one self on both relativistic and quantum Lagrangians, we construct a Lagrangian of relativistic quantum system in one…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum…
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. Covariant equations for this motion are demonstrated to possess pathological solutions, when treated nonperturbatively in…
It is known that any nondegenerate Lagrangian containing time derivative terms higher than first order suffers from the Ostrogradsky instability, pathological excitation of positive and negative energy degrees of freedom. We show that,…
The Euler-Poisson equations para determinar the rotation matrix of a rigid body can be solved without using of particular parameterization like the Euler angles. For the free Lagrange top, we obtain and discuss a general analytic solution,…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The…