30 citations · 112 across the 16 of their papers we have counts for
18 papers
Lagrange points of the restricted three-body problem in spaces of constant curvature
Miguel Ayala, Carlos Barrera-Anzaldo, Luis C. García-Naranjo
We continue the study initiated by Kilin ({\em Reg. Chaot. Dyn.} 4, (1999)) and by Martínez and Simó ({\em Celest. Mech. Dynam. Astronom.} 128, (2017)) on the classification and st…
Abelian instances of nonabelian symplectic reduction
A. Bravo-Doddoli, L. C. García-Naranjo, E. Rigato
Let be a Lie group with a normal abelian subgroup , and let be a symplectic manifold endowed with a Hamiltonian -action. We investigate…
Invariant measures as obstructions to attractors in dynamical systems and their role in nonholonomic mechanics
L. C. García-Naranjo, R. Ortega, A. J. Ureña
We present some rigorous results on the absence of a wide class of invariant measures for dynamical systems possessing attractors. We then consider a generalization of the classica…
Determination of stable branches of relative equilibria of the -vortex problem on the sphere
Kevin Constantineau, Carlos García-Azpeitia, Luis C García-Naranjo +1
We consider the -vortex problem on the sphere assuming that all vorticities have equal strength. We investigate relative equilibria (RE) consisting of latitudinal rings whic…
Platonic solids and symmetric solutions of the -vortex problem on the sphere
Carlos García-Azpeitia, Luis C. García-Naranjo
We consider the -vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion…
Some remarks about the centre of mass of two particles in spaces of constant curvature
Luis C. García-Naranjo
The concept of centre of mass of two particles in 2D spaces of constant Gaussian curvature is discussed by recalling the notion of "relativistic rule of lever" introduced by Galper…
Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics
Luis C. García-Naranjo, Mats Vermeeren
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization…
Attracting and repelling 2-body problems on a family of surfaces of constant curvature
Luis García-Naranjo, James Montaldi
We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric e…
Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
Luis C. García-Naranjo
We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recen…
The geometry of nonholonomic Chaplygin systems revisited
Luis C. García-Naranjo, Juan C. Marrero
We consider nonholonomic Chaplygin systems and associate to them a tensor field on the shape space, that we term the gyroscopic tensor, and that measures the interplay betw…
Generalisation of Chaplygin's Reducing Multiplier Theorem with an application to multi-dimensional nonholonomic dynamics
Luis C. García-Naranjo
A generalisation of Chaplygin's Reducing Multiplier Theorem is given by providing sufficient conditions for the Hamiltonisation of Chaplygin nonholonomic systems with an arbitrary…
Moving energies as first integrals of nonholonomic systems with affine constraints
Francesco Fassò, Luis C. García-Naranjo, Nicola Sansonetto
In nonholonomic mechanical systems with constraints that are affine (linear nonhomogeneous) functions of the velocities, the energy is typically not a first integral. It was shown…
A shortcut to the Kovalevskaya curve
Yu. N. Fedorov, Luis C. García-Naranjo, Joan C. Naranjo
We present a systematic way of derivation of the algebraic curves of separation of variables for the classical Kovalevskaya top and its generalizations, starting from the spectral…
Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2
Luis C. García-Naranjo, Juan C. Marrero, Ernesto Pérez-Chavela +1
We classify and analyze the stability of all relative equilibria for the two-body problem in the hyperbolic space of dimension 2 and we formulate our results in terms of the intrin…
Quasi-periodicity in relative quasi-periodic tori
Francesco Fassò, Luis C. García-Naranjo, Andrea Giacobbe
At variance from the cases of relative equilibria and relative periodic orbits of dynamical systems with symmetry, the dynamics in relative quasi-periodic tori (namely, subsets of…
The inhomogeneous Suslov problem
Luis C. García-Naranjo, Andrzej J. Maciejewski, Juan C. Marrero +1
We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perp…
The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
Yuri N. Fedorov, Luis C. García-Naranjo, Joris Vankerschaver
We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwat…
Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation
Luis C. García-Naranjo, Joris Vankerschaver
We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of…