The equilibrium configurations of the restricted problem of 2+2 triaxial rigid bodies

1995 ◽  
Vol 63 (1) ◽  
pp. 81-100 ◽  
Author(s):  
D. G. Michalakis ◽  
A. G. Mavraganis
Keyword(s):  
Restricted Problem ◽  
Rigid Bodies ◽  
Equilibrium Configurations

INTERNAL CONSTRAINTS AND BIFURCATIONS IN PSEUDO-RIGID BODIES

1996 ◽  
Vol 06 (07) ◽  
pp. 1009-1025
Author(s):  
S. FORTE ◽  
M. VIANELLO
Keyword(s):  
Critical Points ◽  
Rigid Bodies ◽  
The Body ◽  
Stability Of Solutions ◽  
Internal Constraints ◽  
Constraint Manifold ◽  
Order Expansion ◽  
Equilibrium Configurations ◽  
Mathematical Techniques

The equilibrium problem for pseudo-rigid bodies with internal constraints and subject to small loads is discussed. No limitations are placed on the constraints, except for the definitional axiomatic assumptions. Equilibrium configurations are obtained as critical points for a potential defined on the constraint manifold, a Liapunov-Schmidt reduction is performed and a second-order expansion of the reduced potential is obtained. This result is similar to an expansion due to Pierce for unconstrained bodies, but here different mathematical techniques are required. Through a framework which is preserved from the unconstrained theory it is shown that for loads of type 0 the number and stability of solutions is not altered by the introduction of internal constraints. By contrast, differences arise when the body is subjected to loads of type 1.

scholarly journals The Stability of Solutions of Sitnikov Restricted Problem of three Bodies When the Primaries are Triaxial Rigid Bodies

2015 ◽  
Vol 19 (2) ◽  
pp. 76-78
Author(s):  
R.R. Thapa
Keyword(s):  
Restricted Problem ◽  
Principal Axis ◽  
Rigid Bodies ◽  
The Body ◽  
Stability Of Solutions ◽  
Centre Of Mass ◽  
Axis Of Symmetry ◽  
The Stability ◽  
Axes Of Symmetry ◽  
Infinitesimal Mass

The paper deals with the stability of the solutions of Sitnikov's restricted problem of three bodies if the primaries are triaxial rigid bodies. The infinitesimal mass is moving in space and is being influenced by motion of two primaries (m1>m2). They move in circular orbits without rotation around their centre of mass. Both primaries are considered as axis symmetric bodies with one of the axes as axis of symmetry whose equatorial plane coincides with motion of the plane. The synodic system of co-ordinates initially coincides with inertial system of co-ordinates. It is also supposed that initially the principal axis of the body m1 is parallel to synodic axis and are of the axes of symmetry is perpendicular to plane of motion.Journal of Institute of Science and Technology, 2014, 19(2): 76-78

scholarly journals Energy of Sitnikov's restricted three body problem if the primaries are source of radiation and triaxial rigid bodies

BIBECHANA ◽  
2014 ◽  
Vol 12 ◽  
pp. 53-58
Author(s):  
R. R. Thapa
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Equation Of Motion ◽  
Joint Effect ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
The Third ◽  
Three Body

In this paper the joint effect of source of radiation and triaxial rigid body has been studied. The energy of Sitnikov's restricted three body problem when primaries are sources of radiation and energy of Sitnikov's restricted problem of three bodies when primaries are triaxial rigid bodies have been studied to calculate the joint effect. Equation of motion of the third body of infitesimal mass, if primaries are sources of radiation and triaxial rigid bodies,  are calculated.    DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11707BIBECHANA 12 (2015) 53-58

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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