Orbital and Attitude Stability of Space Shuttles in Parking Orbits

1975 ◽  
Vol 26 (1) ◽  
pp. 20-24
Author(s):  
R Arho
Keyword(s):  
Gravitational Field ◽  
Stationary State ◽  
Circular Orbit ◽  
Principal Axis ◽  
Orbital Plane ◽  
Moments Of Inertia ◽  
Attitude Stability ◽  
Principal Moments Of Inertia ◽  
Bounded Perturbation ◽  
The Stability

SummaryA unified treatment is given of the orbital and attitude stability of space shuttles in parking orbits (in vacuo) in the earth’s gravitational field. A shuttle in a circular orbit with a principal axis aligned with the horizontal in the orbital plane is found to be in stationary geostatic equilibrium. The demand for stability leads to a condition which must be satisfied by the principal moments of inertia. The stability which is achieved is not asymptotic without control. The stationary state is a stable centre about which a bounded perturbation oscillation without damping may exist.

An Asymptotic Expansion for

1928 ◽  
Vol 24 (2) ◽  
pp. 280-289 ◽  
Author(s):  
H. P. Mulholland
Keyword(s):  
Vibrational State ◽  
Principal Axis ◽  
The Other ◽  
Band Spectrum ◽  
Molecular Gas ◽  
Moments Of Inertia ◽  
Specific Heats ◽  
Principal Moments Of Inertia ◽  
Adequate Representation ◽  
Image Position

In the theory of the specific heats of gases of diatomic molecules the functionplays a well-known and important part. The rotational specific heat Crot of a diatomic molecule, which is susceptible of representation as a rigid body with two equal principal moments of inertia, without spin about the other principal axis, is given bywhere R is the gram-molecular gas-constant andthe pair of equal moments of inertia being equal to A. Whether such a model is or is not an adequate representation is a matter for determination by a detailed study of the structure of the band spectrum, particularly of the nature of the normal electronic and vibrational state. It is known to be applicable to normal molecules of the halogen hydrides, to CO and other molecules which have a normal state of type 1S including (but for a certain special feature) H2.

Thermal effects on the figure of the Moon

1967 ◽  
Vol 296 (1446) ◽  
pp. 266-269 ◽  
Keyword(s):  
Thermal Effects ◽  
Hydrostatic Equilibrium ◽  
Moment Of Inertia ◽  
The Moon ◽  
Moments Of Inertia ◽  
The Earth ◽  
Principal Moments Of Inertia ◽  
Long Time ◽  
The Stability ◽  
Lunar Rotation

Before discussing its cause, one must be clear in exactly what respect the lunar figure deviates from the equilibrium one. This is necessary because there has been confusion over the question for a long time. It was known early that the Moon’s ellipsoid of inertia is triaxial and that the differences of the principal moments of inertia determined from observations are several times larger than the theoretical values corresponding to hydrostatic equilibrium. The stability of lunar rotation requires that the axis of least moment of inertia point approximately towards the Earth and the laws of Cassini show that it is really so.

EQUILIBRIUM ORBITS OF PARTICLES UNDERGOING POYNTING-ROBERTSON EFFECT IN SCHWARZSCHILD SPACETIME

2012 ◽  
Vol 12 ◽  
pp. 247-255
Author(s):  
DONATO BINI ◽  
ANDREA GERALICO
Keyword(s):  
Angular Momentum ◽  
Gravitational Field ◽  
Radiation Field ◽  
Equatorial Plane ◽  
Circular Orbit ◽  
Radiation Flux ◽  
Multiple Equilibrium ◽  
Schwarzschild Spacetime ◽  
The Stability ◽  
Test Radiation

Equilibrium orbits of particles moving on the equatorial plane of a Schwarzschild spacetime are investigated when a test radiation field is superposed to the background gravitational field. The radiation flux is endowed with a fixed but arbitrary (non-zero) angular momentum. It is found that multiple equilibrium circular orbit exist provided that the photon angular momentum is sufficiently high. The stability of such orbits is also analyzed.

THE STABILITY OF THE UNSYMMETRICAL HEAVY GYRO WITH DAMPING TORQUE

1992 ◽  
Vol 16 (1) ◽  
pp. 83-89
Author(s):  
Zheng-Ming E ◽  
Shih-Ming Chiu
Keyword(s):  
Fixed Point ◽  
Rigid Body ◽  
Direct Method ◽  
Nonlinear Damping ◽  
Center Of Gravity ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Damping Torque

The conditions of the unsymmetrical heavy gyro are that A ≠ B ≠ C where, A, B and C are the principal moments of inertia of the rigid body and the center of gravity G of the rigid body does not coincide with the fixed point, i.e. zc ≠ 0, xc = yc = 0 in this paper. The conditions of the stability and of the instability of the unsymmetrical heavy gyro with and without linear or nonlinear damping torque are obtained by the direct method of Lyapunov.

scholarly journals The Stability Conditions for a Heavy Solid Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
A. I. Ismail
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Sufficient Conditions ◽  
The Body ◽  
Stability Conditions ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Necessary And Sufficient

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z-axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as I 1 < I 2 < I 3 . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

scholarly journals Method for assessment of matching of total ankle joint endoprostheses based on CT data

2020 ◽  
Vol 6 (3) ◽  
pp. 396-397
Author(s):  
Heiner Martin ◽  
Josephine Wittmüß ◽  
Thomas Mittlmeier ◽  
Niels Grabow
Keyword(s):  
Cross Sections ◽  
Spline Functions ◽  
Moments Of Inertia ◽  
Cad System ◽  
Principal Moments Of Inertia ◽  
Principal Axes ◽  
Ct Data ◽  
The One ◽  
Relative Differences ◽  
Systemic Design

AbstractThe investigation of matching of endoprosthesis tibial components to the bone cross section is of interest for the manufacturer as well as for the surgeon. On the one hand, a systemic design of the prosthesis and the assortment is possible, on the other hand, a better matching implantation is enabled on the basis of experience of this study. CT sections were segmented manually using a CAD system and fitted by spline functions, then superseded with cross sections of the tibial component of a modified Hintermann H3 prosthesis. The principal moments of inertia, the direction of the principal axes and the area of the section were evaluated. Based on the relative differences of the principal moments of inertia, recommendations for application of the different prosthesis size and its selection with the surgery can be made.

On the stability of the Earth's gravitational field

1983 ◽  
Vol 26 (2) ◽  
pp. 187-188
Author(s):  
Yu D Bulanzhe ◽  
Yu E Nesterikhin ◽  
N P Pariĭskiĭ
Keyword(s):  
Gravitational Field ◽  
Earth’S Gravitational Field ◽  
The Stability

The whirling of a spinning top

1950 ◽  
Vol 2 (1) ◽  
pp. 9-14
Author(s):  
J. Morris
Keyword(s):  
High Speed ◽  
Moments Of Inertia ◽  
Prime Movers ◽  
Rotating Shafts ◽  
The Common ◽  
The Stability ◽  
Spinning Top

SummaryThis paper has been compiled because of the applicability of the treatment of the stability of the motion of the common spinning top to the problem of the whirling of rotating shafts, carrying loads of appreciable moments of inertia. This problem is assuming renewed interest and importance, especially in the drives of contra-propeller systems and the more recent high speed prime movers.

Orbital dynamics of the gravitational field of stringy black holes

2014 ◽  
Vol 29 (29) ◽  
pp. 1450144 ◽  
Author(s):  
Yu Zhang ◽  
Jin-Ling Geng ◽  
En-Kun Li
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Gravitational Field ◽  
Phase Plane ◽  
Equations Of Motion ◽  
Orbital Dynamics ◽  
Phase Plane Analysis ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
The Stability

In this paper, we study the orbital dynamics of the gravitational field of stringy black holes by analyzing the effective potential and the phase plane diagram. By solving the equation of Lagrangian, the general relativistic equations of motion in the gravitational field of stringy black holes are given. It is easy to find that the motion of test particles depends on the energy and angular momentum of the test particles. Using the phase plane analysis method and combining the conditions of the stability, we discuss different types of the test particles' orbits in the gravitational field of stringy black holes. We get the innermost stable circular orbit which occurs at r min = 5.47422 and when the angular momentum b ≤ 4.3887 the test particles will fall into the black hole.

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