# Hamiltonian Frenet–Serret dynamics

@article{Capovilla2001HamiltonianFD, title={Hamiltonian Frenet–Serret dynamics}, author={Riccardo Capovilla and J. Guven and Efra{\'i}n Rojas}, journal={Classical and Quantum Gravity}, year={2001}, volume={19}, pages={2277-2290} }

The Hamiltonian formulation of the dynamics of a relativistic particle described by a higher derivative action that depends both on the first and the second Frenet–Serret curvatures is considered from a geometrical perspective. We demonstrate how reparametrization covariant dynamical variables and their projections onto the Frenet–Serret frame can be exploited to provide not only a significant simplification of but also novel insights into the canonical analysis. The constraint algebra and the…

## 8 Citations

### Hamiltonian dynamics of extended objects

- Physics
- 2004

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We…

### Null Frenet-Serret dynamics

- Mathematics
- 2006

We consider the Frenet-Serret geometry of null curves in a three and a four-dimensional Minkowski background. We develop a theory of deformations adapted to the Frenet-Serret frame. We exploit it to…

### MECHANICS EQUATIONS OF FRENET-SERRET FRAME ON MINKOWSKI SPACE

- Mathematics
- 2016

It is well known that Minkowski space is the mathematical space setting and Einstein’s theory of special relativity is most appropriate formulated. Dynamical systems theory is an area of mathematics…

### Relativistic Particles along Null Curves in 3D Lorentzian Space Forms

- MathematicsInt. J. Bifurc. Chaos
- 2010

In the case in which Lagrangian density depends quadratically on Cartan curvature, it is shown that the mechanical system is governed by a stationary Korteweg–De Vries system.

### Relativistic particles with rigidity along light-like curves

- Physics, Mathematics
- 2004

We study actions in (2 + 1)-dimensions associated with null curves whose Lagrangians are arbitrary functions f on the curvature of the particle path, showing that null helices are always possible…

### Massless particles in generalized Robertson–Walker 4-spacetimes

- Physics
- 2015

The model of massless relativistic particle relying in a curvature-dependent action functional is considered in the framework of generalized Robertson–Walker 4-spacetimes. The discussion is based on…

### Massless particles in generalized Robertson–Walker 4-spacetimes

- PhysicsAnnali di Matematica Pura ed Applicata (1923 -)
- 2013

The model of massless relativistic particle relying in a curvature-dependent action functional is considered in the framework of generalized Robertson–Walker 4-spacetimes. The discussion is based on…

## References

SHOWING 1-10 OF 52 REFERENCES

### Singular Lagrangians with higher derivatives

- Physics, Mathematics
- 1989

The Hamiltonian formalism for systems with singular Lagrangians of the second order is constructed. A new method is proposed for obtaining the equations of motion in the phase space for theories with…

### Curvature and torsion of the world curve in the action of the relativistic particle

- Physics
- 1991

A generalization of the relativistic particle action is considered. It contains, in addition to the length of the world trajectory, the integrals along the world curve of its curvature and torsion.…

### Dynamics of relativistic particles with Lagrangians dependent on acceleration

- Physics
- 1994

Models of relativistic particles with Lagrangians L(k1), depending on the curvature of the worldline k1, are considered. By making use of the Frenet basis, the equations of motion are reformulated in…

### Extended gauge invariance in geometrical particle models and the geometry of W-symmetry

- Mathematics
- 1995

### MASSIVE RELATIVISTIC POINT PARTICLE WITH RIGIDITY

- Physics
- 1989

The model of relativistic point particle, whose Lagrangian contains a linear dependence on the curvature of the particle world trajectory, is studied. The restriction on the admissible range of…

### Inconsistency of scale-invariant curvature coupled to gravity.

- PhysicsPhysical review letters
- 1990

A physical interpretation of the inconsistency of the scale-invariant curvature action for paths is presented in terms of the nonlocalizability of the photon and a conceptual kinship with the local supersymmetry of a spinning particle is pointed out.