Cristina Stoica
Wilfrid Laurier University
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Featured researches published by Cristina Stoica.
Journal of Mathematical Physics | 1996
Joaquín Delgado; Florin Diacu; Ernesto A. Lacomba; Angelo B. Mingarelli; Vasile Mioc; Ernesto Perez; Cristina Stoica
The Manev problem (a two‐body problem given by a potential of the form A/r+B/r2, where r is the distance between particles and A,B are positive constants) comprises several important physical models, having its roots in research done by Isaac Newton. We provide its analytic solution, then completely describe its global flow using McGehee coordinates and topological methods, and offer the physical interpretation of all solutions. We prove that if the energy constant is negative, the orbits are, generically, precessional ellipses, except for a zero‐measure set of initial data, for which they are ellipses. For zero energy, the orbits are precessional parabolas, and for positive energy they are precessional hyperbolas. In all these cases, the set of initial data leading to collisions has positive measure.
Astrophysics and Space Science | 1997
Cristina Stoica; Vasile Mioc
The Schwarzschild problem (the two-body problem associated to apotential of the form A/r + B/r3 has been qualitativelyinvestigated in an astrophysical framework, exemplified by two likelysituations: motion of a particle in the photogravitational field ofan oblate, rotating star, or in that of a star which generates aSchwarzschild field. Using McGehee-type transformations, regularizedequations of motion are obtained, and the collision singularity isblown up and replaced by the collision manifold λ (a torus)pasted on the phase space. The flow on λ is fullycharacterized. Then, reducing the 4D phase space to dimension 2, theglobal flow in the phase plane is depicted for all possible values ofthe energy and for all combinations of nonzero A and B. Eachphase trajectory is interpreted in terms of physical motion,obtaining in this way a telling geometric and physical picture of themodel.
Journal of Physics A | 2006
Tanya Schmah; Cristina Stoica
In the present paper we apply geometric methods, and in particular the reduced energy–momentum (REM) method, to the analysis of stability of planar rotationally invariant relative equilibria of three-point-mass systems. We analyse two examples in detail: equilateral relative equilibria for the three-body problem, and isosceles triatomic molecules. We discuss some open problems to which the method is applicable, including roto-translational motion in the full three-body problem.
Journal of Nonlinear Science | 2018
Florin Diacu; Cristina Stoica; Shuqiang Zhu
We consider the N-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of effective potential, we define the moment of inertia for systems moving on spheres and hyperbolic spheres and show that we can recover the classical definition in the Euclidean case. After proving some criteria for the existence of relative equilibria, we find a natural way to define the concept of central configuration in curved spaces using the moment of inertia and show that our definition is formally similar to the one that governs the classical problem. We prove that, for any given point masses on spheres and hyperbolic spheres, central configurations always exist. We end with results concerning the number of central configurations that lie on the same geodesic, thus extending the celebrated theorem of Moulton to hyperbolic spheres and pointing out that it has no straightforward generalization to spheres, where the count gets complicated even for two bodies.
arXiv: Dynamical Systems | 2015
Tanya Schmah; Cristina Stoica
We consider free and proper cotangent-lifted symmetries of Hamiltonian systems. For the special case of G = SO(3), we construct symplectic slice coordinates around an arbitrary point. We thus obtain a parameterisation of the phase space suitable for the study of dynamics near relative equilibria, in particular for the Birkhoff-Poincare normal form method. For a general symmetry group G, we observe that for the calculation of the truncated normal forms, one does not need an explicit coordinate transformation but only its higher derivatives at the relative equilibrium. We outline an iterative scheme using these derivatives for the computation of truncated Birkhoff-Poincare normal forms.
Journal of Nonlinear Science | 2014
John A. Arredondo; Ernesto Pérez-Chavela; Cristina Stoica
The Schwarzschild potential, defined as
Physica D: Nonlinear Phenomena | 2010
Daniel Paşca; Manuele Santoprete; Cristina Stoica
Open Astronomy | 1997
Vasile Mioc; Cristina Stoica
U(r)=-A/r-B/r^3
Siam Journal on Applied Dynamical Systems | 2015
Antonio Hernández-Garduño; Cristina Stoica
Nonlinear Analysis-real World Applications | 2009
Manuele Santoprete; Cristina Stoica
U(r)=-A/r-B/r3, where