Angular Momentum in Multiple Rotation Nontwisting Platform Dives

1986 ◽  
Vol 2 (2) ◽  
pp. 78-87 ◽  
Author(s):  
Joseph Hamill ◽  
Mark D. Ricard ◽  
Dennis M. Golden
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Center Of Mass ◽  
Transverse Axis ◽  
Flight Phase ◽  
Local Contribution ◽  
Percent Contribution ◽  
Total Body

A study was undertaken to investigate the changes in total body angular momentum about a transverse axis through the center of mass that occurred as the rotational requirement in the four categories of nontwisting platform dives was increased. Three skilled subjects were filmed performing dives in the pike position, with increases in rotation in each of the four categories. Angular momentum was calculated from the initiation of the dive until the diver reached the peak of his trajectory after takeoff. In all categories of dives, the constant, flight phase total body angular momentum increased as a function of rotational requirement. Increases in the angular momentum at takeoff due to increases in the rotational requirement ranged from a factor of 3.61 times in the forward category of dives to 1.52 times in the inward category. It was found that the remote contribution of angular momentum contributed from 81 to 89% of the total body angular momentum. The trunk accounted for 80 to 90% of the local contribution. In all categories of dives except the forward 1/2 pike somersault, the remote percent contribution of the arms was the largest of all segments, ranging from 38 to 74% of the total angular momentum.

Takeoff Mechanics of the Double Backward Somersault

1990 ◽  
Vol 6 (2) ◽  
pp. 177-186 ◽  
Author(s):  
Inseong Hwang ◽  
Gukung Seo ◽  
Zhi Cheng Liu
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Dominant Role ◽  
Center Of Mass ◽  
Velocity Curve ◽  
The Other ◽  
Transverse Axis ◽  
Angular Momenta ◽  
Total Body ◽  
Direction Opposite

This study examined the biomechanical profiles of the takeoff phase of double backward somersaults in three flight positions: seven layout double backward somersaults (L), seven twisting double backward somersaults (TW), and seven tucked double backward somersaults (TDB). Selected kinematic variables and angular momenta were calculated in order to compare the differences resulting from different aerial maneuvers. The amount of total body angular momentum about the transverse axis through the gymnasts' center of mass progressively increased from TDB to TW to L. The gymnasts performing the skill in the layout position tried to minimize the angle of block in a direction opposite the intended motion by maximizing the angle of touchdown and takeoff. In so doing, the horizontal velocity center-of-mass curve of the L showed a slowly decreasing curve compared with those of the other two somersaults while the vertical velocity curve of the L increased more slowly than the other curves during the takeoff phase. In all cases the legs played the dominant role in contributing to total angular momentum during takeoff.

Complete Shaking Force and Shaking Moment Balancing of Link Mechanisms Using Balancing Idler Loops

1982 ◽  
Vol 104 (2) ◽  
pp. 482-493 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Center Of Mass ◽  
Numerical Example ◽  
Shaking Moment

A method for completely balancing the shaking forces and shaking moments in mechanisms is presented. The method introduces shaking moment balancing idler parallelogram loop (or loops) which transfers the motion of a coupler link to a shaft on the frame of the mechanism, where the rotary balancers balance the shaking moment. The complete balancing of a mechanism is accomplished by maintaining the total center of mass of the mechanism stationary meanwhile achieving that the total angular momentum of the moving links of the mechanism vanishes. Positioning of the idler loops is illustrated for a series of multiloop mechanisms. Theorems on the complete balancing of shaking forces and shaking moments in mechanisms are established. Design equations for completely balancing some single and multiloop mechanisms are given. A numerical example is included.

CENTER OF MASS AND SPIN FOR AXIALLY SYMMETRIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 717-728 ◽  
Author(s):  
CARLOS KOZAMEH ◽  
RAUL ORTEGA ◽  
TERESITA ROJAS
Keyword(s):  
Angular Momentum ◽  
Gravitational Radiation ◽  
Total Angular Momentum ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Intrinsic Angular Momentum

We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

Upper Extremity Function in Running. II: Angular Momentum Considerations

1987 ◽  
Vol 3 (3) ◽  
pp. 242-263 ◽  
Author(s):  
Richard N. Hinrichs
Keyword(s):  
Angular Momentum ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Vertical Component ◽  
The Body ◽  
Lower Trunk ◽  
Body Center ◽  
Recreational Runners ◽  
Total Body ◽  
Angular Impulse

Ten male recreational runners were filmed using three-dimensional cinematography while running on a treadmill at 3.8 m/s, 4.5 m/s, and 5.4 m/s. A 14-segment mathematical model was used to examine the contributions of the arms to the total-body angular momentum about three orthogonal axes passing through the body center of mass. The results showed that while the body possessed varying amounts of angular momentum about all three coordinate axes, the arms made a meaningful contribution to only the vertical component (Hz). The arms were found to generate an alternating positive and negative Hzpattern during the running cycle. This tended to cancel out an opposite Hzpattern of the legs. The trunk was found to be an active participant in this balance of angular momentum, the upper trunk rotating back and forth with the arms and, to a lesser extent, the lower trunk with the legs. The result was a relatively small total-body Hzthroughout the running cycle. The inverse relationship between upper- and lower-body angular momentum suggests that the arms and upper trunk provide the majority of the angular impulse about the z axis needed to put the legs through their alternating strides in running.

Influences of a rider on the rotation of the horse–rider system during jumping

2004 ◽  
Vol 1 (1) ◽  
pp. 33-40 ◽  
Author(s):  
PNR Powers ◽  
AJ Harrison
Keyword(s):  
Angular Momentum ◽  
Angular Velocity ◽  
Repeated Measures ◽  
Total Angular Momentum ◽  
Sagittal Plane ◽  
Repeated Measures Anova ◽  
Flight Phase ◽  
Video Recordings

AbstractThis study examined the effects of a rider on the angular momentum and angular velocity of the jumping horse, particularly during the flight phase. Sagittal plane video recordings were digitized of eight horses jumping a vertical fence (1 m high) under two conditions: Loose and Ridden. An experienced rider rode the horses during the Ridden condition. Using appropriate segmental inertial data for the horse and rider, angular momentum and angular velocity were calculated for the Loose and Ridden conditions. Estimates of the various rider effects on angular momentum and angular velocity were obtained by comparison of Loose and Ridden conditions and examination of the contributions of the horse and rider segments to the total angular momentum. The results showed that the rider's effect on angular momentum was significant but that the rider's segmental contribution to the angular momentum of the horse–rider system was minimal. Repeated-measures ANOVA revealed that the rider had a significant effect on the angular momentum and angular velocity of the horse during the flight phase (P<0.01). However, the rider did not have a significant effect on the transfer of angular momentum during the flight. We concluded that the rider's instruction has a greater influence on the horse's motion than the mechanical transfer between rider and horse.

Greg Louganis’ Springboard Takeoff: II. Linear and Angular Momentum Considerations

1985 ◽  
Vol 1 (4) ◽  
pp. 288-307 ◽  
Author(s):  
Doris I. Miller ◽  
Carolyn F. Munro
Keyword(s):  
Angular Momentum ◽  
Total Angular Momentum ◽  
Center Of Gravity ◽  
Upper Extremities ◽  
Horizontal Velocity ◽  
Initial Contact ◽  
Final Value ◽  
Initial Reduction ◽  
Upward Velocity ◽  
Total Body

A linear and angular momentum analysis was conducted on Greg Louganis' forward and reverse 3-m springboard takeoffs performed during National Sports Festival V in Colorado Springs, and differences among dives were examined. At initial contact with the board, his horizontal velocity approximated 0.5 m/s across all dives analyzed. In the forward 3.5 somersaults pike, the horizontal velocity subsequently increased in magnitude until the latter half of recoil. By contrast, in the forward and reverse dives and reverse 2.5 somersaults, horizontal velocity displayed an initial reduction followed by an increase to the final value of 0.8 to 1.2 m/s. His vertical velocities at touchdown (−4.3 to −4.5 m/s) increased to 5.0 to 6.0 m/s during the takeoff, with the final upward velocity being related to the type of dive performed. At initial contact, Louganis’ total body angular momentum with respect to his center of gravity was negligible. By the end of the takeoff, it had increased to 18 kg-m-m/s for the forward dive straight and was three and four times that magnitude for his reverse 2.5 and forward 3.5 somersaults pike, respectively. Between 80 and 90% of the total angular momentum at the end of the takeoff was due to the segment remote contributions. The importance of the upper extremities in developing somersaulting angular momentum was shown by the fact that they were responsible for between 30 and 43% of the final angular momentum in all but the forward dive straight.

scholarly journals Infrared effects in the late stages of black hole evaporation

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Éanna É. Flanagan
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Center Of Mass ◽  
Planck Scale ◽  
Black Hole Mass ◽  
Order Unity ◽  
Intrinsic Angular Momentum ◽  
Hole Position ◽  
Late Stages ◽  
Shear Tensor

Abstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where Mi is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2 . (iii) The supermomentum and superspin charges are not independent but are determined from the Poincaré charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders l of order unity that are of order unity in Planck units. At large l, there is a power law spectrum of fluctuations that extends up to l ∼ $$ {M}_i^2/M $$ M i 2 / M , beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations ∼ MiM−3/2.

scholarly journals Vertical Jumping for Legged Robot Based on Quadratic Programming

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3679
Author(s):  
Dingkui Tian ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Yizhou Lu ◽  
Chuzhao Liu
Keyword(s):  
Quadratic Programming ◽  
Stance Phase ◽  
Center Of Mass ◽  
Maximum Error ◽  
Legged Robot ◽  
Flight Phase ◽  
Programming Framework ◽  
Vertical Jumping ◽  
Control Schemes ◽  
And Control

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

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