Related papers: False constraints. A toy model for studying dynami…
We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the "wrong sign" for the energy and negative curvature for…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Several simple models of table motion are studied and compared. Dependence of displacement of the table on time,…
Cosmological models involving shear and rotation are considered, first in the General Relat ivistic and then in the Newtonian framework with the aim of investigating singularities in them by using numerical and analytical techniques. The…
Unfortunately, the Hamiltonian mechanics of degenerate Lagrangian systems is usually presented as a mere recipe of Dirac, with no explanation as to how it works. Then it comes to discussing conjectures of whether all primary constraints…
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller…
Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of time machines which can travel forward and…
In the problem of cylinder rolling without slipping on a horizontal floor, both the cylinder and floor are generally treated as rigid bodies in normal textbooks. When the air resistance is ignored, the equation of motion has a solution with…
Quantum systems with constraints are often considered in modern theoretical physcics. All realistic field models based on the idea of gauge symmetry are of this type. A partial case of constraints being linear in coordinate and momenta…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…
Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find…
A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can…
We study the relativistic formulation of a classical time-dependent nonholonomic Lagrangian mechanics from the perspective of moving frames. We also introduce time-dependent $G$-Chaplygin systems with affine constraints, which are natural…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…