scholarly journals Cases of integrability corresponding to the pendulummotion on the plane

2017 ◽  
Vol 21 (10) ◽  
pp. 91-113
Author(s):  
M.V. Shamolin
Keyword(s):  
Rigid Body ◽  
Force Field ◽  
Invariant Form ◽  
Motion Equations ◽  
Plane Parallel ◽  
Free Rigid Body ◽  
Parallel Motion ◽  
Tracking Force ◽  
Similar Force

In this article, we systemize the results on the study of plane-parallel motion equations of fixed rigid body-pendulum which is placed in certain nonconserva- tive force field. In parallel, we consider the problem of a plane-parallel motion of a free rigid body which is also placed in a similar force field. Thus, the non-conservative tracking force operates onto this body. That force forces the value of certain point of a body to be constant for all the time of a motion, which means the existence of nonintegrable servoconstraint in the system. The obtained results are systematized and served in the invariant form. We also show the nontrivial topological and mechanical analogies.

Utilizing the Effort/Motion Approach in the Simulation of Interconnected Rigid Body Systems

1997 ◽  
Author(s):  
N. Duke Perreira
Keyword(s):  
Numerical Simulation ◽  
Rigid Body ◽  
Multibody Systems ◽  
Invariant Form ◽  
Second Law ◽  
Orthogonal Projections ◽  
Gauge Invariant ◽  
Motion Equations ◽  
Newton's Second Law ◽  
Constraint Surface

Abstract The effort/motion approach has been developed for use in designing, simulating and controlling multibody systems. Some aspects of each of these topics are discussed here. In the effort/motion formulation two sets of equations based on the orthogonal projections of a dimensional gauge invariant form of Newton’s Second Law occur. The projections are onto the normal and tangent directions of a dimensional gauge invariant constraint surface. The paper shows how these equations are obtained for a particular linkage with redundant effort and motion actuation. Two alternative Runga-Kutta based approaches for numerical simulation of the effort/motion equations are developed and applied in simulating the motion and determining the effort generated in the example linkage under various conditions. Oscillation about equilibrium positions, solutions with constant motion and with constant effort are given as examples of the approach.

Study of the Rotational Motion of a Rigid Body in Profile School Elective Courses

2016 ◽  
Vol 4 (3) ◽  
pp. 40-45
Author(s):  
Харыбина ◽  
I. Kharybina ◽  
Новикова ◽  
Tatyana Novikova ◽  
Новиков ◽  
...  
Keyword(s):  
Rigid Body ◽  
Conservation Laws ◽  
Rotational Motion ◽  
School Level ◽  
Plane Parallel ◽  
Parallel Motion ◽  
Elective Courses ◽  
Formation Method ◽  
Instantaneous Center ◽  
Physics Course

The article deals with the problem of studying the rotational motion of a rigid body in a physics course at profi le school. It is proposed to supplement the study of the topic elective courses to meet the challenges of the kinematics, dynamics, conservation laws for describing plane-parallel motion of a solid body. The article gives examples of jobs on the formation method of fi nding instantaneous center of velocity, methods are provided for the activities of the students at the school level action.

Noetherian Perspective of Eulerian Motion of a Free Rigid Body

1997 ◽  
Vol 20 (1) ◽  
pp. 193-196
Author(s):  
Yoshihiko Nakamura ◽  
Ranjan Mukherjee
Keyword(s):  
Rigid Body ◽  
Free Rigid Body

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

scholarly journals Combinatory Attitude Determination Method for High Rotational Speed Rigid-Body Aircraft

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Liangliang An ◽  
Liangming Wang ◽  
Ning Liu ◽  
Jian Fu
Keyword(s):  
Rigid Body ◽  
Rotational Speed ◽  
Attitude Determination ◽  
Unscented Kalman Filter ◽  
The State ◽  
Determination Method ◽  
State Equations ◽  
High Rotational Speed ◽  
Motion Equations ◽  
Accuracy Measurement

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

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