Related papers: Frenet-Serret dynamics
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
We propose the model of $D-$dimensional massless particle whose Lagrangian is given by the $N-$th extrinsic curvature of world-line. The system has $N+1$ gauge degrees of freedom constituting $W-$like algebra; the classical trajectories of…
Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…
This paper introduces a novel theoretical framework for identifying Lagrangian Coherent Structures (LCS) in manifolds with non-constant curvature, extending the theory to Finsler manifolds. By leveraging Riemannian and Finsler geometry, we…
A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to…
We revisit the problem of the particle dynamics subject to a geometric holonomic constraint of codimension 1 in spatial dimensions d =2 and 3. In the absence of dissipation, we show that by solving the Lagrangian multiplier in a general…
The Euler-Poincar\'e approach to complex fluids is used to derive multiscale equations for computationally modelling Euler flows as a basis for modelling turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA) which…
By means of the method of moving Frenet-Serret frame the set of equations of motion is derived for spinning particle in an arbitrary external field, which is determined by potential depending from both position and the state of movement, as…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
Inertial motion is considered in the plane of events characterized by the homogeneous Lorentz group L. On the basis of this group, a set of inertial movements and its decomposition into sets which are disconnected from one another with…
Using a Galilean metric approach, based in an embedding of the Euclidean space into a (4+1)-Minkowski space, we analyze a gauge invariant Lagrangian associated with a Riemannian manifold R, with metric g. With a specific choice of the gauge…
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite…
We consider compressible pressureless fluid flows in Lagrangian coordinates in one space dimension. We assume that the fluid self-interacts through a force field generated by the fluid itself. We explain how this flow can be described by a…
The physical phenomena are described by physical quantities related by specific physical laws. In the context of a Physical Theory, the physical quantities and the physical laws are described, respectively, by suitable geometrical objects…
We develop a variational formulation of a particle with spin in a curved space-time background. The model is based on a singular Lagrangian which provides equations of motion, a fixed value of spin and Frenkel condition on spin-tensor.…
We put forward the following, physically motivated premise for constructing a theory that underlies the standard model in four-dimensional space-time: The Euler-Lagrange equations of such a theory formally resemble some equations of motion…
We suggest an alternative mathematical model for the electron in which the dynamical variables are a coframe (field of orthonormal bases) and a density. The electron mass and external electromagnetic field are incorporated into our model by…
A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time…
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…
The phenomenon of gyroscopic precession is studied within the framework of Frenet-Serret formalism adapted to quasi-Killing trajectories. Its relation to the congruence vorticity is highlighted with particular reference to the irrotational…