On the asymptotics of the principal moments of inertia of a convex body in the isotropic state

2021 ◽  
Author(s):  
Vladimir A. Zorich
Keyword(s):  
Convex Body ◽  
Moments Of Inertia ◽  
Isotropic State ◽  
Principal Moments Of Inertia

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 CT sections were segmented manually using a CAD system and fitted by spline functions, then superseded with cross sections of the tibial component of a modified Hintermann H3 prosthesis.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.

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.

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.

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.

scholarly journals Dynamical analysis of a 2-degrees of freedom spatial pendulum

2018 ◽  
Vol 184 ◽  
pp. 01003 ◽  
Author(s):  
Stelian Alaci ◽  
Florina-Carmen Ciornei ◽  
Sorinel-Toderas Siretean ◽  
Mariana-Catalina Ciornei ◽  
Gabriel Andrei Ţibu
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Dynamical Analysis ◽  
Analysis Software ◽  
Lagrange Equations ◽  
Moments Of Inertia ◽  
Dynamical Simulation ◽  
Principal Moments Of Inertia

A spatial pendulum with the vertical immobile axis and horizontal mobile axis is studied and the differential equations of motion are obtained applying the method of Lagrange equations. The equations of motion were obtained for the general case; the only simplifying hypothesis consists in neglecting the principal moments of inertia about the axes normal to the oscillation axes. The system of nonlinear differential equations was numerically integrated. The correctness of the obtained solutions was corroborated to the dynamical simulation of the motion via dynamical analysis software. The perfect concordance between the two solutions proves the rightness of the equations obtained.

The Bending of Pretwisted Thin-Walled Beams of Symmetric Star-Shaped Cross Sections

1958 ◽  
Vol 25 (1) ◽  
pp. 67-74
Author(s):  
L. Maunder
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Energy Methods ◽  
Approximate Analysis ◽  
Moments Of Inertia ◽  
Elastic Bending ◽  
Principal Moments Of Inertia ◽  
Equivalent Bending Stiffness ◽  
Symmetric Star ◽  
Thin Walled

Abstract The customary method of determining the elastic bending deflections of pretwisted beams predicts that the deflections of a uniform beam with a cross section having equal principal moments of inertia will be independent of pretwist. Experimental deflections of a thin-walled pretwisted beam with a doubly symmetric cruciform cross section have been found, however, to be significantly larger than those thus predicted. Based on energy methods, an approximate analysis is developed for pretwisted thin-walled beams having symmetric star-shaped cross sections, which takes into account the effect of interactions between pretwist and distortions of cross sections. An equivalent bending stiffness is derived which is a function of pretwist. The principal theoretical and experimental results are shown in Fig. 4.

Topics in Gyroscopic Motion

1953 ◽  
Vol 20 (1) ◽  
pp. 1-8
Author(s):  
H. Poritsky
Keyword(s):  
Kinetic Equations ◽  
Spin Axis ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
Gyroscopic Motion

Abstract After a brief review of the fundamental kinetic equations of gyroscope motion, the following topics are considered: (a) The erection of an electrically driven gyroscope when an electrical torque is applied. (b) The effect of inequality of the principal moments of inertia normal to the spin axis, on gyroscope motion. (c) The effect of inertia of the gimbals on motion of the gyroscope.

Pretwisted Beams and Columns

1956 ◽  
Vol 23 (2) ◽  
pp. 165-175
Author(s):  
John Zickel
Keyword(s):  
Cross Section ◽  
Buckling Load ◽  
Structural Members ◽  
Moments Of Inertia ◽  
Principal Moments Of Inertia ◽  
Constant Rate ◽  
Thin Walled ◽  
The Cross ◽  
Stiffening Factor

Abstract A theory is developed for the behavior of pretwisted structural members of thin-walled section with slight initial bending. The stresses are at first determined along and perpendicular to the fibers and are then transformed to stresses in the cross section and along the axis. Although the development is perfectly general the integrations are only indicated for doubly symmetric sections. The buckling of doubly symmetric columns which are initially straight but are pretwisted at a constant rate is treated in detail. The results show that columns of decidedly unequal principal moments of inertia can be strengthened up to 90 per cent, but columns of equal moments of inertia are weakened by initial twist. In analogy to the Euler load of the buckling theory for straight, untwisted columns, a reduced Euler load is defined. The buckling load is the product of this reduced Euler load and a stiffening factor.

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