Inelastic Cable-connected Satellites System under Several Influences of General Nature: Equations of Motion in Elliptical Orbit

In the present work, we have applied the analytical approach to obtain the equations of motion of a system of two cable connected artificial satellites under the effect of various perturbative forces of general nature. These perturbative forces are the earth’s shadow, solar radiation pressure, earth’s oblateness and the earth’s magnetic field. Our aim is to investigate the motion of the centre of mass of the two artificial cable connected satellite system in Keplerian elliptical orbit. We establish the equations of motion for the centre of mass of the system and also for the relative motion of the system. We obtain equations of motion in the rotating frame of reference as well as in Nechvile’s co-ordinate system. The cable under consideration is light, flexible, non-conducting and elastic in nature.

Download Full-text

Plane wave propagation in a rotating anisotropic medium with voids under the action of a uniform magnetic field

International Journal of Computational Materials Science and Engineering ◽

10.1142/s2047684116500159 ◽

2016 ◽

Vol 05 (03) ◽

pp. 1650015

Author(s):

Narottam Maity ◽

S. P. Barik ◽

P. K. Chaudhuri

Keyword(s):

Magnetic Field ◽

Wave Propagation ◽

Plane Wave ◽

Equations Of Motion ◽

Magnetic Field Effect ◽

General Nature ◽

Linear Elastic ◽

Paper Plane ◽

Constant Magnitude ◽

Plane Wave Propagation

In this paper, plane wave propagation in a rotating anisotropic material of general nature under the action of a magnetic field of constant magnitude has been investigated. The material is supposed to be porous in nature and contains voids. Following the concept of [Cowin S. C. and Nunziato, J. W. [1983] “Linear elastic materials with voids,” J. Elasticity 13, 125–147.] the governing equations of motion have been written in tensor notation taking account of rotation, magnetic field effect and presence of voids in the medium and the possibility of plane wave propagation has been examined. A number of particular cases have been derived from our general results to match with previously obtained results in this area. Effects of various parameters on the velocity of wave propagation have been presented graphically.

Download Full-text

On the Stability of Periodic Motions of a Two-Body SystemWith Flexible Connection in an Elliptical Orbit

10.21203/rs.3.rs-297984/v1 ◽

2021 ◽

Author(s):

Xue Zhong ◽

Jie Zhao ◽

Kaiping Yu ◽

Minqiang Xu

Keyword(s):

Periodic Solutions ◽

Fourth Order ◽

Equations Of Motion ◽

Center Of Mass ◽

Elliptical Orbit ◽

Periodic Motions ◽

Nonlinear Stability Analysis ◽

The Third ◽

The Stability ◽

Lyapunov Instability

Abstract This paper deals with periodic motions and their stability of a flexible connected two-body system with respect to its center of mass in a central Newtonian gravitational field on an elliptical orbit. Equations of motion are derived in a Hamiltonian form and two periodic solutions as well as the necessary conditions for their existence are acquired. By analyzing linearized equations of perturbed motions, Lyapunov instability domains and domains of stability in the first approximation are obtained. In addition, the third and fourth order resonances are investigated in linear stability domains. A constructive algorithm based on a symplectic map is used to calculate the coeffcients of the normalized Hamiltonian. Then a nonlinear stability analysis for two periodic solutions is performed in the third and fourth order resonance cases as well as in the nonresonance case.

Download Full-text

Dynamics of Systems That Include Wings in Autorotation

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2802462 ◽

1999 ◽

Vol 121 (2) ◽

pp. 248-254 ◽

Cited By ~ 2

Author(s):

D. Seter ◽

A. Rosen

Keyword(s):

Equations Of Motion ◽

Rigid Bodies ◽

General Nature ◽

Aerodynamic Loads ◽

Multibody Model ◽

Euler Approach ◽

Theoretical Results ◽

Rotor Model ◽

Good Agreement ◽

Blade Element

A general multibody model, appropriate for investigating the autorotation of various systems of rigid bodies, is presented. Using the Newton-Euler approach, a generic modular matrix form of the equations of motion is obtained. The general nature of this detailed, nonlinear model allows the description of a large variety of autorotating systems. The calculations of the aerodynamic loads that act on the blades include the use of empirical data combined with an extended blade element/momentum analysis. The model is first validated by comparing its results with analytical results for simple cases. Then the use of the model to investigate the autorotation of a rotor model in a wind tunnel is presented. Good agreement between the experimental and theoretical results is shown.

Download Full-text

The equations of motion of a secularly precessing elliptical orbit

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/sts239 ◽

2012 ◽

Vol 428 (3) ◽

pp. 2605-2616

Author(s):

S. Casotto ◽

M. Bardella

Keyword(s):

Equations Of Motion ◽

Elliptical Orbit

Download Full-text

Non-linear Planar Oscillation of a Satellite in Elliptical Orbit Under the Influence of External Forces of General Nature

Astrophysics and Space Science Library - Space Dynamics and Celestial Mechanics ◽

10.1007/978-94-009-4732-0_28 ◽

1986 ◽

pp. 295-307

Author(s):

R. B. Singh

Keyword(s):

Elliptical Orbit ◽

General Nature ◽

Non Linear ◽

External Forces

Download Full-text

The motion of a lunar orbiter

Symposium - International Astronomical Union ◽

10.1017/s0074180900105686 ◽

1966 ◽

Vol 25 ◽

pp. 373

Author(s):

Y. Kozai

Keyword(s):

Degrees Of Freedom ◽

Dimensional Space ◽

Artificial Satellite ◽

Equations Of Motion ◽

Triaxial Ellipsoid ◽

The Moon ◽

Secular Motion ◽

The Earth ◽

Close Satellite ◽

The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Download Full-text

On the motion of comet P/d’Arrest

International Astronomical Union Colloquium ◽

10.1017/s025292110003387x ◽

1974 ◽

Vol 22 ◽

pp. 145-148

Author(s):

W. J. Klepczynski

Keyword(s):

Equations Of Motion ◽

Variational Equations ◽

Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

Download Full-text

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

Tire Science and Technology ◽

10.2346/1.3130984 ◽

2009 ◽

Vol 37 (2) ◽

pp. 62-102 ◽

Cited By ~ 3

Author(s):

C. Lecomte ◽

W. R. Graham ◽

D. J. O’Boy

Keyword(s):

Internal Pressure ◽

Equations Of Motion ◽

Three Dimensional ◽

Prediction Method ◽

Analytical Models ◽

Beam Model ◽

Impedance Boundary ◽

Bending Waves ◽

Tire Rotation ◽

Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

Download Full-text

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

Tire Science and Technology ◽

10.2346/1.3481649 ◽

2010 ◽

Vol 38 (3) ◽

pp. 182-193 ◽

Cited By ~ 1

Author(s):

Gary E. McKay

Keyword(s):

System Performance ◽

Equations Of Motion ◽

Test Laboratory ◽

Excellent Correlation ◽

Friction Behavior ◽

Aircraft Landing ◽

Data Scatter ◽

Tire Forces ◽

Six Degree Of Freedom ◽

Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

Download Full-text