A Study on Mixed Kinetic-Kinematic Equations for Multibody Systems

2013 ◽  
Author(s):  
Sung-Soo Kim ◽  
Bongcheol Seo ◽  
Myungho Kim
Keyword(s):  
Angular Velocity ◽  
Velocity Vector ◽  
Reference Frames ◽  
Time Derivative ◽  
Kinetic Equations ◽  
Angular Acceleration ◽  
The Body ◽  
Integration Step ◽  
Angular Velocity Vector ◽  
The Relationship

In this paper, mixed kinetic-kinematic equations for a multibody system have been studied in order to resolve the difficulties of non-integrability of angular velocity vectors. As for the kinetic equations, the Newton-Euler equations of motion are considered. They are derived in terms of angular velocity and angular acceleration vectors expressed in the body fixed reference frames. As for the kinematic compatibility equations, two different equations are considered. One is from the relationship between the angular velocity vector and the time derivatives of Euler parameters. The other is from the relationship between the rotational orientation matrix, its time derivative, and the angular velocity vector. In order to investigate the accuracy of the solution methods using two different kinematic compatibility equations, simulations of a spherical pendulum model and a 1/6 robot vehicle model have been carried out. With different integration step-sizes, the constraint violation errors have been also investigated.

scholarly journals On the Geodetic Rotation of the Major Planets, the Moon and the Sun

2009 ◽  
Vol 44 (2) ◽  
pp. 43-52
Author(s):  
G. Eroshkin ◽  
V. Pashkevich
Keyword(s):  
Angular Velocity ◽  
Reference Frame ◽  
Velocity Vector ◽  
Previous Investigation ◽  
The Body ◽  
The Other ◽  
The Sun ◽  
The Moon ◽  
Angular Velocity Vector

On the Geodetic Rotation of the Major Planets, the Moon and the SunThe problem of the geodetic (relativistic) rotation of the major planets, the Moon and the Sun was studied in the paper by Eroshkin and Pashkevich (2007) only for the components of the angular velocity vectors of the geodetic rotation, which are orthogonal to the plane of the fixed ecliptic J2000. This research represents an extension of the previous investigation to all the other components of the angular velocity vector of the geodetic rotation, with respect to the body-centric reference frame from Seidelmann et al. (2005).

scholarly journals On New Modifications of Some Perturbation Procedures

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
A. I. Ismail
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
The Body ◽  
Large Parameter ◽  
Angular Velocity Vector ◽  
Rigid Body Dynamic ◽  
Motion Problem ◽  
Slow Motions ◽  
Body Dynamic

In this paper, we present new modifications for some perturbation procedures used in mathematics, physics, astronomy, and engineering. These modifications will help us to solve the previous problems in different sciences under new conditions. As problems, we have, for example, the rotary rigid body problem, the gyroscopic problem, the pendulum motion problem, and other ones. These problems will be solved in a new manner different from the previous treatments. We solve some of the previous problems in the presence of new conditions, new analysis, and new domains. We let complementary conditions of such studied previously. We solve these problems by applying the large parameter technique used by assuming a large parameter which inversely proportional to a small quantity. For example, in rigid body dynamic problems, we take such quantity to be one of the components of the angular velocity vector in the initial instant of the rotary body about a fixed point. The domain of our solutions will be depending on the choice of a large parameter. The problem of slow (weak) oscillations is considered. So, we obtain slow motions of the bodies instead of fast motions and find the solutions of the problem in present new conditions on both of center of gravity, moments of inertia, and the angular velocity vector or one of these parameters of the body. This study is important for aerospace engineering, gyroscopic motions, satellite motion which has the correspondence of inertia moments, antennas, and navigations.

Kinematics of rotation in place during defense turning in the crayfish Procambarus clarkii

2001 ◽  
Vol 204 (3) ◽  
pp. 471-486 ◽  
Author(s):  
N. Copp ◽  
M. Jamon
Keyword(s):  
Angular Velocity ◽  
Procambarus Clarkii ◽  
Angular Acceleration ◽  
The Body ◽  
Simple Variation ◽  
Freely Behaving ◽  
Leg Motion ◽  
Two Phases ◽  
Analysis System ◽  
Final Orientation

The kinematic patterns of defense turning behavior in freely behaving specimens of the crayfish Procambarus clarkii were investigated with the aid of a video-analysis system. Movements of the body and all pereiopods, except the chelipeds, were analyzed. Because this behavior approximates to a rotation in place, this analysis extends previous studies on straight and curve walking in crustaceans. Specimens of P. clarkii responded to a tactile stimulus on a walking leg by turning accurately to face the source of the stimulation. Angular velocity profiles of the movement of the animal's carapace suggest that defense turn responses are executed in two phases: an initial stereotyped phase, in which the body twists on its legs and undergoes a rapid angular acceleration, followed by a more erratic phase of generally decreasing angular velocity that leads to the final orientation. Comparisons of contralateral members of each pair of legs reveal that defense turns are affected by changes in step geometry, rather than by changes in the timing parameters of leg motion, although inner legs 3 and 4 tend to take more steps than their outer counterparts during the course of a response. During the initial phase, outer legs 3 and 4 exhibit larger stance amplitudes than their inner partners, and all the outer legs produce larger stance amplitudes than their inner counterparts during the second stage of the response. Also, the net vectors of the initial stances, particularly, are angled with respect to the body, with the power strokes of the inner legs produced during promotion and those of the outer legs produced during remotion. Unlike straight and curve walking in the crayfish, there is no discernible pattern of contralateral leg coordination during defense turns. Similarities and differences between defense turns and curve walking are discussed. It is apparent that rotation in place, as in defense turns, is not a simple variation on straight or curve walking but a distinct locomotor pattern.

Sensor Placement for Angular Velocity Determination

2005 ◽  
Vol 128 (3) ◽  
pp. 543-547 ◽  
Author(s):  
Guy M. Genin ◽  
Joseph Genin
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
Constraint Equation ◽  
Complete Characterization ◽  
Angular Velocity Vector ◽  
Algebraic Constraint ◽  
Transducer Placement

Velocity transducer placement to uniquely determine the angular velocity of a rigid body is investigated. The angular velocity of a rigid body can be determined with no fewer than five properly placed velocity transducers, if no other types of sensors are present and no algebraic constraint equation involving the angular velocity vector can be written. Complete characterization of the velocity of a rigid body requires six transducers. Choice of transducer placement and orientation requires care, as suboptimal transducer placement can result in data from which the determination of a unique angular velocity vector is impossible. Conditions for successful transducer placement are established, and two examples of adequate transducer placement are presented: an Earth-penetrating projectile, and a bioengineering device for the measurement of head motion.

Development of angular velocity vector measurement of a spherical rotor based on color sensors

2017 ◽  
Vol 40 (13) ◽  
pp. 3736-3743
Author(s):  
ChengGang Pan ◽  
GaoFei Zhang
Keyword(s):  
Angular Velocity ◽  
Attitude Control ◽  
Velocity Vector ◽  
Spherical Surface ◽  
Contact Method ◽  
Angular Velocity Vector ◽  
Loop Control ◽  
Direction Error ◽  
Black And White ◽  
Color Sensors

Spherical actuators have many applications in satellite attitude control. It is very important for closed-loop control to measure the angular velocity vector of the spherical rotor accurately and quickly. This paper proposes one non-contact method for measuring angular velocity vector of a spherical rotor, using four color sensors. The spherical rotor surface should be color-coded with red, blue, green, magenta, yellow, cyan, black and white, while each color covers an octant in sequence. Four color sensors are mounted about the vertexes of a tetrahedron, used to sense the color of the spherical surface and transform them into angular velocity vector. Simulations approve the correctness of this method, within a module error of approximately 5.2 rpm and a direction error of 0.88 degree within 4000 rpm. Experiments verify that the random error is smaller than 2.7 rpm and direction error smaller than 1.1 degree within 2000 rpm.

Kinematics of an Elastic Sphere Rolling on a Plane and Between Two Planes

1993 ◽  
Vol 115 (3) ◽  
pp. 476-480
Author(s):  
E. Kingsbury
Keyword(s):  
Angular Velocity ◽  
Elastic Deformation ◽  
General Expression ◽  
Velocity Vector ◽  
Elastic Sphere ◽  
Angular Velocity Vector ◽  
Spiral Path ◽  
Symmetry Argument

A sphere rolling between a stationary and a spinning plane traces out a spiral path, even under quasistatic conditions. Published theory suggests that radial creep due to pivot produces the spiral path. We show experimentally a component of the sphere’s angular velocity not considered in the published analysis, raising questions about pivot in producing the spiral. We give a general expression for the sphere angular velocity vector which accommodates a linear, circular or spiral path, pivot or no pivot, and one or two planes in contact. We show that a sphere can roll in a circle on one or between two plane without pivot, but not between a stationary and a spinning plane. We show that a circumferential component of angular velocity results in a spiral path. A symmetry argument suggests that the spiral might be due to elastic deformation in the planes rather than to pivot, but the question is still open.

Algorithm of the Time-Optimal Reorientation of an Axially Symmetric Spacecraft in the Class of Conical Motions

2018 ◽  
Vol 19 (12) ◽  
pp. 10-17587/mau.19.797-805
Author(s):  
Ya. G. Sapunkov ◽  
A. V. Molodenkov ◽  
T. V. Molodenkova
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Velocity Vector ◽  
Space Shuttle ◽  
Control Function ◽  
Axially Symmetric ◽  
Bounded Control ◽  
Angular Velocity Vector ◽  
Time Optimal ◽  
Optimal Turn

The problem of the time-optimal turn of a spacecraft as a rigid body with one axis of symmetry and bounded control function in absolute value is considered in the quaternion statement. For simplifying problem (concerning dynamic Euler equations), we change the variables reducing the original optimal turn problem of axially symmetric spacecraft to the problem of optimal turn of the rigid body with spherical mass distribution including one new scalar equation. Using the Pontryagin maximum principle, a new analytical solution of this problem in the class of conical motions is obtained. Algorithm of the optimal turn of a spacecraft is given. An explicit expression for the constant in magnitude optimal angular velocity vector of a spacecraft is found. The motion trajectory of a spacecraft is a regular precession. The conditions for the initial and terminal values of a spacecraft angular velocity vector are formulated. These conditions make it possible to solve the problem analytically in the class of conical motions. The initial and the terminal vectors of spacecraft angular velocity must be on the conical surface generated by arbitrary given constant conditions of the problem. The numerical example is presented. The example contain optimal reorientation of the Space Shuttle in the class of conical motions.

Some Dimensions of the Angular Acceleration Receptor Systems of Cephalopods

1984 ◽  
Vol 64 (1) ◽  
pp. 55-79 ◽  
Author(s):  
Linda Maddock ◽  
J. Z. Young
Keyword(s):  
Angular Velocity ◽  
Frequency Band ◽  
Deep Sea ◽  
Horizontal Plane ◽  
Angular Acceleration ◽  
The Body ◽  
The Other ◽  
Radius Of Curvature ◽  
Internal Radius ◽  
Neutrally Buoyant

The shapes and dimensions of the statocysts of cephalopods have been measured and compared with the semi-circular canals of vertebrates. The cavities grow much more slowly than the body as a whole, but there are knobs, anticristae, which restrict the cavity, and these grow relatively faster. This ensures that the flow of endolymph across the cupulae remains small. Where the liquid is constrained within canals the radius of curvature of the whole canal, R, is similar to that of fishes, whereas its internal radius, r, is twice as large in non-buoyant and four times as large in deep-sea buoyant cephalopods as in fishes of similar size. As in fishes the restriction is greatest in the horizontal plane, providing for operation at higher frequencies in turning about the yaw axis.The statocysts of seven species of Loligo all have similar proportions. The largest individuals of 16 genera of non-buoyant squids also have these same relative dimensions. The statocyst of Sepia is more like that of non-buoyant than of other buoyant cephalopods but yet differs significantly from that of Loligo at all sizes. On the other hand 21 genera of squids known to be neutrally buoyant are very different. Their statocysts are often larger than in the non-buoyant forms and there is less restriction of the cavity by anticristae. The greater flow of endolymph acting across the cupulae presumably provides greater sensitivity at the lower frequencies of turning of these deep-sea animals.The data suggest that the cristae of the cephalopod statocyst may operate in the frequency band where they act as angular accelerometers whereas the vertebrate semi-circular canals operate at higher frequencies as angular velocity meters.

Sign in / Sign up

Export Citation Format

Share Document