Alexei A. Deriglazov
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View article: Improved Equations of the Lagrange Top and Examples of Analytical Solutions
Improved Equations of the Lagrange Top and Examples of Analytical Solutions Open
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagona…
View article: Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions
Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions Open
Euler–Poisson equations of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles …
View article: Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions
Rotation Matrix of a Charged Symmetrical Body: One-Parameter Family of Solutions in Elementary Functions Open
Euler-Poisson equations of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles …
View article: An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect
An asymmetrical body: example of analytical solution for the rotation matrix in elementary functions and Dzhanibekov effect Open
We solved the Poisson equations, obtaining their exact solution in elementary functions for the rotation matrix of a free asymmetrical body with angular velocity vector lying on separatrices. This allows us to discuss the temporal evolutio…
View article: Poincaré–Chetaev Equations in Dirac’s Formalism of Constrained Systems
Poincaré–Chetaev Equations in Dirac’s Formalism of Constrained Systems Open
We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket. …
View article: Dynamics on a submanifold: intermediate formalism versus Hamiltonian reduction of Dirac bracket, and integrability
Dynamics on a submanifold: intermediate formalism versus Hamiltonian reduction of Dirac bracket, and integrability Open
We consider Hamiltonian formulation of a dynamical system forced to move on a submanifold $G_α(q^A)=0$. If for some reasons we are interested in knowing the dynamics of all original variables $q^A(t)$, the most economical would be a Hamilt…
View article: Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions
Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions Open
Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point, imme…
View article: Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system Open
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulate…
View article: Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?
Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures? Open
We have revised the problem of the motion of a heavy symmetric top. When formulating equations of motion of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in …
View article: Lagrange top: integrability according to Liouville and examples of analytic solutions
Lagrange top: integrability according to Liouville and examples of analytic solutions Open
Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagona…
View article: Has the problem of the motion of a heavy symmetric top been solved in quadratures?
Has the problem of the motion of a heavy symmetric top been solved in quadratures? Open
We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the litera…
View article: Geodesic motion on the symplectic leaf of $$SO(3)$$ with distorted e(3) algebra and Liouville integrability of a free rigid body
Geodesic motion on the symplectic leaf of $$SO(3)$$ with distorted e(3) algebra and Liouville integrability of a free rigid body Open
The solutions to the Euler–Poisson equations are geodesic lines of SO (3) manifold with the metric determined by inertia tensor. However, the Poisson structure on the corresponding symplectic leaf does not depend on the inertia tensor. We …
View article: General solution to the Euler-Poisson equations of a free Lagrange top directly for the rotation matrix
General solution to the Euler-Poisson equations of a free Lagrange top directly for the rotation matrix Open
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,…
View article: Poincaré-Chetaev equations in the Dirac's formalism of constrained systems
Poincaré-Chetaev equations in the Dirac's formalism of constrained systems Open
We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket. …
View article: Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and Liouville integrability of a free rigid body
Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and Liouville integrability of a free rigid body Open
The solutions to the Euler-Poisson equations are geodesic lines of $SO(3)$ manifold with the metric determined by the inertia tensor. However, the Poisson structure on the corresponding symplectic leaf does not depend on the inertia tensor…
View article: Comment on the Letter "Geometric Origin of the Tennis Racket Effect'' by P. Mardesic, et al, Phys. Rev. Lett. 125, 064301 (2020)
Comment on the Letter "Geometric Origin of the Tennis Racket Effect'' by P. Mardesic, et al, Phys. Rev. Lett. 125, 064301 (2020) Open
In the recent work [1], authors discussed the relationship between the two of Euler angles assuming that it can be used to describe some effects in the theory of a rigid body. I show that this assumption is not properly justified.
View article: Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system Open
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulate…
View article: Basic Notions of Poisson and Symplectic Geometry in Local Coordinates, with Applications to Hamiltonian Systems
Basic Notions of Poisson and Symplectic Geometry in Local Coordinates, with Applications to Hamiltonian Systems Open
This work contains a brief and elementary exposition of the foundations of Poisson and symplectic geometries, with an emphasis on applications for Hamiltonian systems with second-class constraints. In particular, we clarify the geometric m…
View article: Spinning gravimagnetic particles in Schwarzschild-like black holes
Spinning gravimagnetic particles in Schwarzschild-like black holes Open
We study the motion of a spinning particle with gravimagnetic moment in\nSchwarzschild-like spacetimes with a metric $ds^2=-f(r) dt^2 + f^{-1}(r) dr^2 +\nr^2 d\\Omega^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom\nblack h…
View article: Spinning gravimagnetic particles in Schwarzschild-like black holes
Spinning gravimagnetic particles in Schwarzschild-like black holes Open
We study the motion of a spinning particle with gravimagnetic moment in Schwarzschild-like spacetimes with a metric $ds^2=-f(r) dt^2 + f^{-1}(r) dr^2 + r^2 dΩ^2$, specifically we deal with Schwarzschild, Reissner-Nordstrom black holes as w…
View article: Comment on "Frame-dragging: meaning, myths, and misconceptions" by L. F.\n O. Costa and J. Nat\\'ario
Comment on "Frame-dragging: meaning, myths, and misconceptions" by L. F.\n O. Costa and J. Nat\\'ario Open
I point out that the authors' interpretation of their calculations differs\nfrom the standard interpretation, described in Sect. 84 of Landau-Lifshitz\nbook. This casts doubt on the authors' claim that Sagnac effect "arises also in\nappara…
View article: Comment on "Frame-dragging: meaning, myths, and misconceptions" by L. F. O. Costa and J. Natário
Comment on "Frame-dragging: meaning, myths, and misconceptions" by L. F. O. Costa and J. Natário Open
I point out that the authors' interpretation of their calculations differs from the standard interpretation, described in Sect. 84 of Landau-Lifshitz book. This casts doubt on the authors' claim that Sagnac effect "arises also in apparatus…
View article: Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime
Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime Open
We present the manifestly covariant Lagrangian of a massless polarized\nparticle, that implies all dynamic and algebraic equations as the conditions of\nextreme of this variational problem. The model allows for minimal interaction\nwith a …
View article: Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin
Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin Open
We show that there is a manifestly covariant version of the Pauli Hamiltonian\nwith equations of motion quadratic on spin and field strength. Relativistic\ncovariance inevitably leads to noncommutative positions: classical brackets of\nthe…
View article: Acceleration of particles in Schwarzschild and Kerr geometries
Acceleration of particles in Schwarzschild and Kerr geometries Open
The Landau-Lifshitz decomposition of spacetime, or (1+3)-split, determines the three-dimensional velocity and acceleration as measured by static observers. We use these quantities to analyze the geodesic particles in Schwarzschild and Kerr…