Internal Mass Motion Research Articles

PERTURBED MOTIONS OF A NEARLY DYNAMICALLY SPHERICAL RIGID BODY WITH A MOVABLE MASS SUBJECT TO CONSTANT BODY-FIXED TORQUE

The problem of motion of a rigid body about a fixed point is one of the classical problems of mechanics. The interest to the problems of the rigid body dynamics has increased in the second half of the XX century in connection with the development of rocket and space technologies. A spacecraft or satellite, while orbiting about its center of mass, experiences torques from forces of diverse physical nature. This includes torques generated by the motion of internal masses, which can arise from factors such as presence of rotating components (like rotors or gyroscopes), and the activities of crew members aboard the crew vehicle. The dynamics of rigid body incorporated moving masses is a significant focal point in classical mechanics. Extensive research is dedicated to investigating the rotation of a rigid body featuring motion of internal masses. It is assumed that the body contains a viscoelastic element that is modeled by a moving mass connected to the body by a strong damper. The moving mass model loosely attached elements in a space vehicles, which can significantly affect the vehicle’s motion about its center of mass during a long period of time. Some cases are considered of the motion of a rigid body containing internal masses connected to the body by means of elastic and dissipative elements. A number of works are devoted to the analysis of various problems of the dynamics of space vehicles containing internal movable masses. The paper develops an approximate solution by means of averaging method to the system of Euler’s equation terms for a nearly dynamically spherical rigid body containing a viscoelastic element under the action of constant body-fixed torque. We obtained the system of motion equations in the standard form which refined in square-approximation by small parameter. Asymptotic approach permits to obtain some qualitative results and to describe evolution of angular motion using simplified averaged equations and numerical solution. The main objective of this paper is to extend the previous results for the problem of motion about a center of mass of a rigid body under the influence of small internal torque (cavity filled with a fluid of high viscosity) or external torque (resistive medium). The importance of the results is in progress of moving mass control motion of spinning projectiles.

Plane-parallel motion of a trimaran capsubot controlled with an internal flywheel

Swimming robots driven by internal mass motion are demanded for applications in aggressive media. A novel type of such robot is proposed – a trimaran controlled by a single internal flywheel. The robot consists of a platform, three blades rigidly connected to it, and a flywheel located at the platform. A control torque is applied to the flywheel. The control is the sum of periodic excitation and feedback terms. It provides oscillations of the flywheel. Oscillations of the flywheel cause oscillations of the platform with blades. Oscillating blades submerged in fluid provide the thrust force. The mathematical model of the system is constructed basing on the quasi-steady description of hydrodynamic loads. Parameters of the control law are adjusted to increase the propulsion speed. It is shown that the lateral force acting on each blade plays crucial role in the propulsion. In a wide range of parameters, the system possesses two types of attracting periodic modes of propulsion: high-speed bow-first motion and low-speed stern-first motion. Both these modes are irreversible with respect to the main direction of propulsion. The self-start of the robot to a high-speed mode depends on geometrical parameters and on the control law. The laboratory prototype of the robot is constructed.

Locomotion analysis of self-propelled board by inclined internal mass motion with slider-crank mechanism

Locomotion analysis of self-propelled board by inclined internal mass motion with slider-crank mechanism

Dissipation and mass redistribution as a mechanism of propulsion in closed systems

In this work, the mechanism behind motion in closed systems is investigated by studying two simple mechanical systems. Firstly, a simple “ballistic” car system introduces the subject of propulsion as a function of a parameter that modulates the amount of ejected mass, thus allowing a transition between a closed to an open system. The second example provides a physically realizable (and optimizable) system, in which a mass sliding on the internal surface of a mechanical wheeled cavity is shown to produce a net movement, provided that dissipation is present. Several additional ways are discussed by which to ‘open’ a system whilst keeping the mass constant. As a function of strict momentum conservation, it is concluded that both internal mass motion and dissipation are key factors in the only way a mechanical system can move itself in a weak sense, in contrast to a strong meaning of ‘self-propulsion’.

Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body

This paper addresses the problem of a rigid body moving on a plane (a platform) whose motion is initiated by oscillations of a point mass relative to the body in the presence of the viscous friction force applied at a fixed point of the platform and having in one direction a small (or even zero) value and a large value in the transverse direction. This problem is analogous to that of a Chaplygin sleigh when the nonholonomic constraint prohibiting motions of the fixed point on the platform across the direction prescribed on it is replaced by viscous friction. We present numerical results which confirm correspondence between the phenomenology of complex dynamics of the model with a nonholonomic constraint and a system with viscous friction — phase portraits of attractors, bifurcation diagram, and Lyapunov exponents. In particular, we show the possibility of the platform’s motion being accelerated by oscillations of the internal mass, although, in contrast to the nonholonomic model, the effect of acceleration tends to saturation. We also show the possibility of chaotic dynamics related to strange attractors of equations for generalized velocities, which is accompanied by a two-dimensional random walk of the platform in a laboratory reference system. The results obtained may be of interest to applications in the context of the problem of developing robotic mechanisms for motion in a fluid under the action of the motions of internal masses.

Optimal Motions of Bodies Controlled by Internal Moving Masses

Abstract Locomotion of robots in a resistive medium can be based on special motions of auxiliary internal masses inside the main body of the robot. This locomotion principle is used in micro-robots and vibro-robots moving in tubes. In the paper, optimal motions of systems controlled by internal moving masses are considered. One-dimensional optimal motions are examined for systems moving in the presence of dry friction forces. Two-dimensional motions are considered for bodies subject to dry friction and containing internal moving masses. Optimal motions of a two-body system are obtained for the case where external forces are negligible. This situation is a model for the re-orientation of a spacecraft containing a moving internal mass.

Motion by variation of the contact force on an inclined plane

AbstractThis paper describes non‐classical locomotion based on the variation of the contact force. The motion of a locomotion system on an inclined plane is considered. The contact force between the locomotion system and the inclined plane can be influenced by the motion of internal masses. Therefore a mechanical model with two internal masses is introduced. The friction between the locomotion system and the environment is described by COULOMB's law. The motion of this locomotion system is investigated and analyzed by using the averaging method of BOGOLJUBOV and MITROPOLSKI. Furthermore the influence of different parameters on the locomotion characteristics like the direction of movement, the stationary velocity and the maximum inclination angle is shown. A prototype based on this locomotion principle is built up for experimental investigations. Additionally, simulations are used to analyze the locomotion system. The experimental values are compared to the theoretically results and confirm the variation of the contact force as an option to enable a controlled locomotion. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Моделирование перемещения клиновидного виброробота в вязкой жидкости при различных законах движения внутренней массы в пакете OpenFOAM

The work is devoted to the study of the two-mass vibration-driven system motion in the viscous fluid. The system consists of a closed wedge-shaped body, placed in a fluid, and a movable internal mass, oscillated harmonically inside the shell. The described mechanical system simulates a vibration-driven robot. The complex model of the robot interaction with the medium is considered, where fluid motion is described by the full unsteady Navier-Stokes equations. The problems of improving the efficiency of vibration-driven robot motion by choosing a special law internal mass movement are investigated. For these purposes, a comparative analysis of the characteristics of the motion and flow regimes around the robot are carried out for the simple harmonic law of the internal mass motion and the special two-phase law of the internal mass motion. The analysis of the flows around the robot and their influence on the characteristics (the average speed and the efficiency) of the movement is carried out. The numerical solution of the problem is carried out in the OpenFOAM open-source software package. The numerical scheme is implemented on the basis of the finite-volume discretization approach. For joint solution the Navier-Stokes equations and the mechanical system, which describes the interaction of components of vibration-driven robot and viscous media, a special iteration scheme is constructed. Results of the study show that the directional movement of the wedge-shaped vibration-driven robot is possible for both harmonic and two-phase laws of internal mass motion. In each of the cases it is possible to find stable regimes of motion observed in a wide range of Reynolds numbers. Analysis of average speed and efficiency of regimes allows finding the optimal parameters of vibration-driven robot motion.

Two-dimensional motions of a body containing internal moving masses

Movement of a body inside a resistive medium can be based on special vibrational motions of internal masses contained within this body. This principle of movement does not require any external devices such as wheels, legs, or tracks interacting with the outer environment; the system can be hermetic. This type of mobile systems sometimes called vibro-robots or capsubots can be useful for motions inside hazardous or vulnerable media and inside tubes. In the literature, one-dimensional motions of such systems were studied in various resistive media. In the paper, two-dimensional motions of a multibody mobile system carrying internal masses are analyzed in the presence of dry friction forces acting between the system and the horizontal plane. It is shown that, under certain conditions, this system can be brought from any initial position to the prescribed terminal position in the plane. The algorithm of motion is described and specified.

Rotation of the body with movable internal masses around the center of mass on a rough plane

We consider the motion of a system consisting of a rigid body and internal movable masses on a rough surface. The possibility of rotation of the system around its center of mass due to the motion of internal movable masses is investigated. To describe the friction between the body and the reference surface, a local Amontons-Coulomb law is selected. To determine the normal stress distribution in the contact area between the body and the surface, a linear dynamically consistent model is used. As examples we consider two configurations of internal masses: a hard horizontal disk and two material points, which move parallel to the longitudinal axis of the body symmetry in the opposite way. Motions of the system are analyzed for selected configurations.

Rotation of a body with two movable internal masses on a rough plane

The two-dimensional motion of a system consisting of a hollow rigid body, resting on a rough plane, and two internal mobile point masses, capable of moving parallel to the longitudinal axis of symmetry of the body is considered. Friction in the contact area is modelled by a local Amonton–Coulomb law. A dynamically matched linear model is used to describe the normal stress distribution. The possibility of achieving rotation of the system by a certain relative motion of internal masses is investigated. Two control laws for the movable masses are considered: piecewise-linear and harmonic, for which the equations of motion are integrated numerically for different values of the parameters of the control laws. The features of the motion of the system for the chosen laws are analysed. It is established that, for a two-phase piecewise-linear control law, rotation of the system reaches a steady state. The parameters of the piecewise-linear control law, which deliver a maximum of the mean angular velocity of the body in the steady mode of motion are obtained.

Stability of Spinning Satellite Under Axial Thrust, Internal Mass Motion, and Damping

The paper extends and clarifies the stability results for a spinning satellite under axial thrust in the presence of internal damped mass motion. It is known that prolate and oblate satellite configurations can be stabilized by damped mass motion. Here, the stability boundaries are established by exploiting the properties of the complex characteristic equation and the results are interpreted in terms of the physical system parameters. When the thrust level is the only free parameter, both prolate and oblate satellites can be stabilized provided that the thrust is within a specified range. This result is in contrast to the well-known maximum-axis rule for a free spinner where damping is always stabilizing (destabilizing) for an oblate (prolate) satellite. When adding a suitable spring-mass system, the minimum value of the spring constant that stabilizes the configuration can be established. In practice, however, the damping may well be too weak to be effective. Numerical illustrations are presented for the actual parameters of the Ulysses prolate configuration at orbit injection as well as for a fictitious oblate system. Finally, a new derivation of a previously established first integral for the undamped system is offered and its properties as a Lyapunov function are discussed.

Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization

Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.

Stability of spinning satellite under axial thrust and internal mass motion

This paper considers a spinning rigid body and a particle with internal motion under axial thrust. This model is helpful for gaining insights into the nutation anomalies that occurred near the end of orbit injections performed by STAR-48 rocket motors. The stability of this system is investigated by means of linearized equations about a uniform spin reference state. In this model, a double root does not necessarily imply instability. The resulting stability condition defines a manifold in the parameter space. A detailed study of this manifold and the parameter space shows that the envelope of the constant solutions is in fact the stability boundary. Only part of the manifold defines a physical system and the range of frequency values that make the system unstable is restricted. Also it turns out that an increase of the spring stiffness, which restrains the internal motion, does not necessarily increase the stability margin. The application of the model is demonstrated using the orbit injection data of ESA's Ulysses satellite in 1990.

Dynamic modeling and motion simulation for a winged hybrid-driven underwater glider

PETREL, a winged hybrid-driven underwater glider is a novel and practical marine survey platform which combines the features of legacy underwater glider and conventional AUV (autonomous underwater vehicle). It can be treated as a multi-rigid-body system with a floating base and a particular hydrodynamic profile. In this paper, theorems on linear and angular momentum are used to establish the dynamic equations of motion of each rigid body and the effect of translational and rotational motion of internal masses on the attitude control are taken into consideration. In addition, due to the unique external shape with fixed wings and deflectable rudders and the dual-drive operation in thrust and glide modes, the approaches of building dynamic model of conventional AUV and hydrodynamic model of submarine are introduced, and the tailored dynamic equations of the hybrid glider are formulated. Moreover, the behaviors of motion in glide and thrust operation are analyzed based on the simulation and the feasibility of the dynamic model is validated by data from lake field trials.

Motion of a mechanism along a rough inclined plane using the motion of internal oscillating masses

A mobile mechanism capable of moving along a rough plane inclined surface using the motion of internal masses according to the harmonic law is considered. Oscillations of internal masses have equal frequencies and different phases. It is shown that using this principle of motion the mechanism can move upward along an inclined plane. Maximization conditions of the established motion velocity are given.

Two Successive Coronal Mass Ejections Driven by the Kink and Drainage Instabilities of an Eruptive Prominence

We describe a clear case of the initiation of a propagating bright arc and a CME on 2002 December 28, which were associated with an eruptive prominence. In EIT 304 and 195 8 images, a very long filament showed evidence of severe twisting in one of its fragments, which appeared as a prominence on December 26; then, the prominence showed the conversion of its twist into writhe. Two days later, the prominence displayed a slow rising motion for hours. Internal twisting and mass motion took place before the rapid acceleration and final eruption. The propagating bright arc and the following CME corresponded to the early rising and the subsequently eruptive phases of the prominence, respectively. Signatures of magnetic reconnection, i.e., a cusp structure and postflare loops in EUV wave bands and hard X-ray sources in the corona, were observed after the prominence eruption. It appears that the kink instability and the mass drainage in the prominence played key roles in triggering the initiation of the CME. However, the rather impulsive acceleration of the CME resulted from magnetic reconnection beneath the filament.

CMEs driven by an eruptive prominence

A clear case on Dec. 28 2002 is presented. It is about the initiation of two successive CMEs, which were related to an eruptive prominence. In EIT 304 Å and 195 Å observations, we found a long filament severely twisting in a piece of its fragments, which appeared as a prominence on Dec. 26. Then, the prominence converted its twist into writhe. Two days later, the prominence displayed a slow rising motion for hours. There happened internal twisting and mass motion before the prominence rapid acceleration and final eruption. Two successive CMEs recorded by LASCO C2 coronagraph corresponded to the early rising and the subsequently eruptive phases of the prominence, respectively. Evidence of magnetic reconnection, i.e., a cusp structure and post-flare loops in EUV wavebands, and hard X-ray sources in the corona, were observed after the prominence disruption. It appears that the kink instability and the mass drainage in the prominence played important roles in triggering two CMEs' initiation. We suspected that the rather impulsive acceleration of the second CME resulted from magnetic reconnection beneath the prominence.

Attitude Control of a Rhönrad by Internal Mass Motion

Rhonrad is a gymnastic equipment that is interesting in terms of dynamics and control. The control method of the Spiral motion by the mass motion in the Rhonrad was clarified. First, the condition for a steady Spiral motion with arbitrary mass position was obtained. Then, by using the linearized equation of motion, the control method to control the attitude of the Rhonrad by the mass motion in it was derived. This control method allows the state of the Rhonrad to be changed from one steady Spiral motion to another steady motion.

Control of motion of an inhomogeneous cylinder with internal movable masses along a horizontal plane

The controlled motion of a rigid inhomogeneous cylinder over a rough horizontal plane is considered. The control is provided by controlled motion of internal masses. Mathematical models are constructed that correspond to rolling without loss of contact or slippage. The conditions for the physical implementability of such a motion are derived. The case where the internal moving masses from a rigid flywheel the centre of inertia of which lies on the axis of the cylinder is investigated in detail. A near-time-optimal feedback control that enables the total energy to be changed in a required way is constructed on the basis of an asymptotic approach. The main operating modes are simulated, namely, swinging up of the cylinder to a large angular amplitude, rotation with a prescribed energy, deceleration of rolling to a complete stop, and oscillations and rotations in the neighbourhood of the separatrix.