Head and Trunk Segment Moments of Inertia Estimation Using Angular Momentum Technique: Validity and Sensitivity Analysis

2011 ◽  
Vol 58 (5) ◽  
pp. 1278-1285 ◽  
Author(s):  
M Damavandi ◽  
G Stylianides ◽  
N Farahpour ◽  
P Allard
Keyword(s):  
Sensitivity Analysis ◽  
Angular Momentum ◽  
Moments Of Inertia ◽  
Trunk Segment

scholarly journals Equivalence of Euler equations and torque-angular momentum relation

2021 ◽  
Vol 18 (1) ◽  
pp. 136
Author(s):  
V. Tanriverdi
Keyword(s):  
Angular Momentum ◽  
Rigid Body ◽  
Reference Frame ◽  
Euler Equations ◽  
Equations Of Motion ◽  
The Body ◽  
Moments Of Inertia ◽  
Body Reference ◽  
Stationary Reference Frame ◽  
Momentum Relation

Euler derived equations for rigid body rotations in the body reference frame and in the stationary reference frame by considering an infinitesimal part of the rigid body.Another derivation is possible, and it is widely used: transforming torque-angular momentum relation to the body reference frame.However, their equivalence is not shown explicitly.In this work, for a rigid body with different moments of inertia, we calculated Euler equations explicitly in the body reference frame and in the stationary reference frame and torque-angular momentum relation.We also calculated equations of motion from Lagrangian.These calculations show that all four of them are equivalent.

Optimal System Values for Producing a Large Velocity of the Distal Endpoint during Flail-Like Motion

2002 ◽  
Vol 18 (3) ◽  
pp. 278-286 ◽  
Author(s):  
Michele LeBlanc ◽  
Jesús Dapena
Keyword(s):  
Sensitivity Analysis ◽  
Angular Momentum ◽  
Angular Velocity ◽  
Optimal Parameter ◽  
Single Equation ◽  
Kinetic Chain ◽  
Human Arm ◽  
Large Velocity ◽  
System Variables ◽  
Parameter Values

Equations that clarify the mechanical relationships between various parameter values and the velocity of the distal endpoint of a two-segment kinetic chain modeling the human arm were developed and analyzed. In particular, a single equation was presented that relates the distal endpoint velocity to the system’s angular momentum (as an indicator of muscular torque input), the ratio of the distal segment’s angular velocity to that of the proximal segment (the flail ratio), and the angle between the two segments (the configuration angle). These three system variables were analyzed to examine which values are best for creating a large value for the velocity of the distal endpoint. In addition, a sensitivity analysis was conducted to determine whether the relationships between the system values and the distal endpoint velocity were consistent for varying segment parameters. The relationships found were consistent for the various segment parameters. For any given values of the flail ratio and the configuration angle, the larger the value of the system angular momentum, the larger the value of the distal endpoint velocity. For any given values of the system angular momentum and the configuration angle, the larger the flail ratio, the larger the value of the distal endpoint velocity. For given values of the system angular momentum and the flail ratio, the optimal configuration angle that maximizes the distal endpoint velocity depends on the flail ratio value. While it may be impossible to generate simultaneously the combination of optimal parameter values determined, the knowledge of the relationships of these parameters with each other and with the distal endpoint velocity will aid in the search for an attainable optimal compromise.

The G-Band Systematics of Vibrational and Transitional Nuclei with A = 150 to 166

1994 ◽  
Vol 49 (7-8) ◽  
pp. 802-810
Author(s):  
M. I. El-Zaiki ◽  
H. E. Abdel-Baeth
Keyword(s):  
Angular Momentum ◽  
Central Region ◽  
Spectrum Analysis ◽  
Band Spectrum ◽  
Shape Transition ◽  
Moments Of Inertia ◽  
Shell Closures ◽  
Major Shell ◽  
Cubic Polynomial ◽  
Band Crossing

Abstract The vibrational and rotational characteristics of the ground bands of even-even nuclei with 150 ≤ A ≤ 166 (2 < R4< 3) are studied. The spectra of these nuclei (with band crossing angular momentum IC ≥ 12) are analyzed with a cubic polynomial in I. The considered nuclei (150Sm, 152Gd, 154-156Dy, 156Er, 158-160-162Yb and 162,164, 166Hf) lie in the central region between the Z = 50 and Z = 82 major shell closures and span the spherical to the well deformed region. The gradual shape transition from a soft spherical vibrator to a deformed rotor from 150Sm to 166Hf is thus made explicitly apparent from the g-band spectrum analysis in terms of the vibrational, rotational and softness coefficients.The transition at N = 88-90 for the vibrational-rotational ratios and for the kinematic moments of inertia are reproduced.

Zur Theorie der Kernrotationen II

1961 ◽  
Vol 16 (10) ◽  
pp. 1077-1082
Author(s):  
Hans Hackenbroich
Keyword(s):  
Angular Momentum ◽  
Binding Energies ◽  
Strength Parameter ◽  
Expectation Values ◽  
Nuclear Moments ◽  
Moments Of Inertia ◽  
Correct Sequence ◽  
The Difference ◽  
The One ◽  
Nuclear Levels

The effect of residual interactions in the Inglis model of nuclear rotations is discussed. The interactions are idealized as contactpotentials, and the one particle potentials are taken from Nilsson. In this model the expectation values of the residual interactions cannot be approximated by the “pairing energies”, i.e. the binding energies of particles in the same orbit but with opposite z-components of angular momentum. For the nuclei calculated (156Gd, 157Gd, 158Gd) the residual interactions reduce the nuclear moments of inertia. However, with the strength parameter of the interactions set in order to obtain the correct sequence of nuclear levels, the calculated moments of inertia are still greater than the observed ones. The model cannot explain the difference between the moments of inertia of even and odd nuclei.

Dynamic rotational characteristics of actinides on empirical approach

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Maria Kaczmarczyk ◽  
Andrzej Korejwo
Keyword(s):  
Experimental Data ◽  
Angular Momentum ◽  
Ground Level ◽  
Analytical Form ◽  
Moment Of Inertia ◽  
Relative Deviation ◽  
Moments Of Inertia ◽  
Rotational States ◽  
The Moment ◽  
Experimental Values

AbstractIn the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.

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