Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

2007 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Center Of Mass ◽  
Solution Process ◽  
Body System ◽  
Efficient Treatment ◽  
Composite Body ◽  
Recursive Solution ◽  
System A ◽  
Principal Axes ◽  
Solution Methods ◽  
Treat All

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest are the reaction wheels in satellites, wheels on a car, propellers on a helicopter and flywheels in machines. Each such body spins about one of its principal axes and around its center of mass. Current recursive solution methods treat all bodies in the system identically. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order O(N-m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Center Of Mass ◽  
Solution Process ◽  
Body System ◽  
Efficient Treatment ◽  
Composite Body ◽  
Recursive Solution ◽  
System A ◽  
Principal Axes ◽  
Solution Methods ◽  
The Moment

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an N-body system. The bodies of interest include the reaction wheels in satellites, wheels on a car, and flywheels in machines. More specifically, these bodies have diagonal inertia tensors. They spin about one of its principal axes, with the moment of inertia along the transverse axes identical. Their center of mass lies on the spin axis. Current recursive solution methods treat these bodies identically as any other body in the system. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the order(N−m) where m is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA

2000 ◽  
Vol 10 (05) ◽  
pp. 997-1018 ◽  
Author(s):  
M. IÑARREA ◽  
V. LANCHARES
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Center Of Mass ◽  
Melnikov Method ◽  
Moments Of Inertia ◽  
Suitable Parameter ◽  
Nutation Angle ◽  
Principal Axes ◽  
Reorientation Process ◽  
Subharmonic Resonances

We study the spin-up dynamics of a dual-spin spacecraft containing one axisymmetric rotor which is parallel to one of the principal axes of the spacecraft. It will be supposed that one of the moments of inertia of the platform is a periodic function of time and that the center of mass of the spacecraft is not modified. Under these assumptions, it is shown that in the absence of external torques and spinning rotors the system possesses chaotic behavior in the sense that it exhibits Smale's horseshoes. We prove this statement by means of the Melnikov method. The presence of chaotic behavior results in a random spin-up operation. This randomness is visualized by means of maps of the initial conditions with final nutation angle close to zero. This phenomenon is well described by a suitable parameter that measures the amount of randomness of the process. Finally, we relate this parameter with the Melnikov function in the absence of the spinning rotor and with the presence of subharmonic resonances.

Spin Rotor Stabilization of a Dual-Spin Spacecraft with Time Dependent Moments of Inertia

1998 ◽  
Vol 08 (03) ◽  
pp. 609-617 ◽  
Author(s):  
V. Lanchares ◽  
M. Iñarrea ◽  
J. P. Salas
Keyword(s):  
Periodic Function ◽  
Center Of Mass ◽  
The Body ◽  
Body Motion ◽  
Time Dependent ◽  
Moments Of Inertia ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Principal Axes

We consider a dual-spin deformable spacecraft, in the sense that one of the moments of inertia is a periodic function of time such that the center of mass is not altered. In the absence of external torques and spin rotors, by means of the Melnikov's method we prove that the body motion is chaotic. Stabilization is obtained by means of a spinning rotor about one of the principal axes of inertia.

Application of a MIMO-PID Controller for a Hydraulic Excavator Considering the Velocity of CoM

2020 ◽  
Vol 32 (3) ◽  
pp. 643-651
Author(s):  
Masatoshi Kozui ◽  
Toru Yamamoto ◽  
Masaki Akiyama ◽  
Kazushige Koiwai ◽  
Yoichiro Yamazaki ◽  
...  
Keyword(s):  
Control System ◽  
High Efficiency ◽  
Population Aging ◽  
Center Of Mass ◽  
Hydraulic Excavator ◽  
Skilled Workers ◽  
Construction Sites ◽  
System A ◽  
Hydraulic Excavators ◽  
Recent Trends

There are many machines that require human operation in industry, and high operational skills are required to operate these machines efficiently. However, the number of highly skilled workers is decreasing due to the recent trends of falling birthrate and population aging. This decline is particularly pronounced in the construction industry, while the demand for construction workers remains high owing to the increasing number of developed infrastructures. To reduce this mismatch between the supply and the demand, it is important to achieve high efficiency in tasks using hydraulic excavators, because these machines can greatly increase the productivity at construction sites. Accordingly, it is necessary to improve productivity even if unskilled operators use hydraulic excavators. This paper proposes a control system that achieves efficient motions based on the velocity of the center of mass (CoM) of the hydraulic excavator’s attachments, which reflects the characteristics of skilled workers’ operations. The motions of multiple attachments give rise to interference terms owing to the characteristics of the hydraulic system. A two-input two-output control system, in which the input consists of the lever input and the output is the CoM velocity is constructed. The fictitious reference iterative tuning (FRIT) method is used to calculate the controller parameters. The proposed method was verified by comparing the results of a simulated digging motion and an experiment with an actual hydraulic excavator operated by an unskilled operator.

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