New Formulation of de Sitter’s Theory of Motion for Jupiter I–IV. I. Equations of Motion and the Disturbing Function

1978 ◽  
pp. 189-206
Author(s):  
K. Aksnes
Keyword(s):  
Equations Of Motion ◽  
Disturbing Function ◽  
Theory Of Motion ◽  
New Formulation

scholarly journals New Formulation of De Sitter’s Theory of Motion for Jupiter I-IV. I. Equations of Motion and the Disturbing Function

1978 ◽  
Vol 41 ◽  
pp. 189-206
Author(s):  
K. Aksnes
Keyword(s):  
Equations Of Motion ◽  
Disturbing Function ◽  
De Sitter ◽  
Retrograde Motion ◽  
Canonical Variables ◽  
Relative Coordinates ◽  
Delaunay Variables ◽  
New Formulation ◽  
Basic Features ◽  
Poincaré Variables

AbstractA brief discussion is given of the basic features of de Sitter’s theory. The main advantage of his theory is that it contains no small divisors, thanks to the use of elliptic rather than circular intermediate orbits in the first approximation. A 50-year extension of the satellite observations available to de Sitter makes it desirable to rederive the elements of his intermediate orbits, whose perijoves have a common retrograde motion. Furthermore, the theory suffers from a convergence problem, which can be avoided by reformulating the theory in terms of canonical variables, a task that is begun here. We adopt a formulation in Poincaré’s canonical relative coordinates rather than, as customary, in ordinary relative coordinates or in the Jacobian canonical coordinates. By means of the generalized Newcomb operators devised by Izsak, the disturbing function is expanded in a form that is very convenient for use with the modified Delaunay variables, G, L – G, H – G, l + ω + Ω, l, and ω and their associated Poincaré variables.

scholarly journals New Approach to the Planetary Theory

1979 ◽  
Vol 81 ◽  
pp. 69-72 ◽  
Author(s):  
Manabu Yuasa ◽  
Gen'ichiro Hori
Keyword(s):  
Perturbation Method ◽  
Canonical Form ◽  
Equations Of Motion ◽  
Disturbing Function ◽  
Averaging Principle ◽  
The Sun ◽  
Planetary Theory ◽  
New Approach ◽  
Canonical Perturbation ◽  
Relative Coordinates

A new approach to the planetary theory is examined under the following procedure: 1) we use a canonical perturbation method based on the averaging principle; 2) we adopt Charlier's canonical relative coordinates fixed to the Sun, and the equations of motion of planets can be written in the canonical form; 3) we adopt some devices concerning the development of the disturbing function. Our development can be applied formally in the case of nearly intersecting orbits as the Neptune-Pluto system. Procedure 1) has been adopted by Message (1976).

A New Approach on Object Slippage Control in a Cooperating Manipulators System

2007 ◽  
Author(s):  
Shahram Hadian Jazi ◽  
Mehdi Keshmiri ◽  
Farid Sheikholeslam
Keyword(s):  
Dynamic Modeling ◽  
Equations Of Motion ◽  
Friction Model ◽  
System Stability ◽  
Order System ◽  
Control Synthesis ◽  
Modeling And Control ◽  
Cooperating Manipulators ◽  
End Effectors ◽  
New Formulation

Considering slippage in the end-effectors of a set of two cooperating manipulators grasping an object, this paper presents a new dynamic modeling and control synthesis of grasping phenomenon. This dynamic modeling is based on a new formulation for frictional contact where equality and inequality equations in the standard Coulomb Friction model are converted all to a single second order differential equation with switching coefficients. Accuracy of the friction model is verified by comparing its results with those of SimMech. Then equations of motion are reduced to conventional form for nonconstrained system. Assuming the new reduced order system to be BIBO, internal stability of the whole system is analyzed. In the control synthesis of the system a multi phase controller is utilized to control the trajectory tracking of the object as well as slippage control of the end-effectors on the object surfaces. For the proposed controller, a proof is given for system stability and its performance and robustness are shown numerically. The results show superiority of the method and its desirable and excellent performance.

scholarly journals Binary Asteroids: Secular Perturbations

1992 ◽  
Vol 152 ◽  
pp. 183-184
Author(s):  
R. Vilhena De Moraes ◽  
S. M. G. Winter
Keyword(s):  
Equations Of Motion ◽  
Disturbing Function ◽  
Binary Asteroids ◽  
Small Bodies ◽  
Secular Perturbations

The motion of two small bodies orbiting each other whose barycenter is orbiting around a massive body is studied. The equations of motion are integrated considering the secular part of the disturbing function.

scholarly journals On the ‘Thermodynamics’ of Self-Gravitating N-Body Systems

1974 ◽  
Vol 62 ◽  
pp. 261-272
Author(s):  
R. H. Miller
Keyword(s):  
Transfer Rate ◽  
Canonical Ensemble ◽  
Equations Of Motion ◽  
High Rate ◽  
Body System ◽  
Energy Transfer Rate ◽  
Transfer Energy ◽  
Unusual Behavior ◽  
Gravitating Systems ◽  
New Formulation

Results of some simple ‘thermodynamic’ experiments on self-gravitating n-body systems are reported for a variety of boundary conditions. Systems placed in specularly reflecting enclosures did not show any unusual behavior, even though a variety of conditions was tried in an attempt to start a ‘gravothermal castastrophe’. Similarly, there was no tendency to transfer energy between ‘hot’ and ‘cool’ subclosures within a given cluster. However, systems in ‘isothermal’ enclosures gave up energy to the enclosure at a surprisingly high rate, and sustained the energy-transfer rate as long as the experiment was continued. An explanation of these different behaviors was sought and found in an examination of the premises that underlie certain attempts to construct a thermodynamics for self-gravitating systems. Conventional application of the H-theorem implies violations of the n-body equations of motion and predictions not consistent with observation. Both the ‘gravothermal catastrophe’ and the experiments in an ‘isothermal’ enclosure share this violation of the equations of motion. A new formulation that allows for all the interactions in an n-body system shows that isolated n-body systems need not form binaries or condense into other subaggregates. The virial theorem follows as an ensemble average over the micro-canonical ensemble.

Application of the Vector-Network Method to Constrained Mechanical Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 471-480 ◽  
Author(s):  
Tai-Wai Li ◽  
Gordon C. Andrews
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Computer Applications ◽  
Kinematic Chains ◽  
Constrained Mechanical Systems ◽  
3 Dimensional ◽  
Methodical Approach ◽  
Dynamic Formulation ◽  
Reaction Forces ◽  
New Formulation

The vector-network technique is a methodical approach to formulating equations of motion for unconstrained dynamic systems, utilizing concepts from graph theory and vectorial mechanics; it is ideally suited to computer applications. In this paper, the vector-network theory is significantly improved and extended to include constrained mechanical systems with both open and closed kinematic chains. A new formulation procedure is developed in which new kinematic constraint elements are incorporated. The formulation is based on a modified tree/cotree classification, which deviates significantly from previous work, and reduces the number of equations of motions to be solved. The dynamic equations of motion are derived, with generalized accelerations and a subset of the reaction forces as solution variables, and a general kinematic analysis procedure is also developed, similar to that of the dynamic formulation. Although this paper restricts most discussions to two-dimensional (planar) systems, the new method is equally applicable to 3-dimensional systems.

On a new field theory formulation and a space-time adjustment that predict the same precession of Mercury and the same bending of light as general relativity

2020 ◽  
Vol 33 (4) ◽  
pp. 489-512
Author(s):  
Larry M. Silverberg ◽  
Jeffrey W. Eischen
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Equations Of Motion ◽  
Space Time ◽  
Undergraduate College Student ◽  
Continuity Equations ◽  
Theory Formulation ◽  
New Formulation ◽  
Gravitational Problem ◽  
Bending Of Light

This article introduces a new field theory formulation. The new field theory formulation recognizes vector continuity as a general principle and begins with a field that satisfies vector continuity equations. Next, independent of the new formulation, this article introduces a new space-time adjustment. Then, we solve the one-body gravitational problem by applying the space-time adjustment to the new field theory formulation. With the space-time adjustment, the new formulation predicts precisely the same precession of Mercury and the same bending of light as general relativity. The reader will find the validating calculations to be simple. The equations of motion that govern the orbital equations are in terms of Cartesian coordinates and time. An undergraduate college student, with direction, can perform the validations.

On the Use of Virtual Work in a Graph-Theoretic Formulation for Multibody Dynamics

1997 ◽  
Author(s):  
Pengfei Shi ◽  
John McPhee
Keyword(s):  
Multibody Systems ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Theoretic Approach ◽  
Computer Implementation ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Flexible Multibody ◽  
New Formulation

Abstract In this paper, graph-theoretic and virtual work methods are combined in a new formulation of the equations of motion for rigid and flexible multibody systems. In addition to extending the theory for existing graph-theoretic approaches, this new formulation offers two distinct improvements. First, the set of differential-algebraic dynamic equations are smaller in number than those obtained using conventional formulations. Secondly, the equations of motion for rigid and flexible multibody systems can be generated using a consistent graph-theoretic approach, thereby leading to an efficient and modular computer implementation.

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