scholarly journals On the relations between kinetic energy and linear momentum, angular momentum of the particle and of the rigid body

2001 ◽  
Vol 23 (2) ◽  
pp. 110-115
Author(s):  
Nguyen Van Khang
Keyword(s):  
Angular Momentum ◽  
Kinetic Energy ◽  
Rigid Body ◽  
Partial Derivative ◽  
Multibody Systems ◽  
Linear Momentum ◽  
Dynamics Of Multibody Systems

Using the definition for the partial derivative of a scalar in respect to the vector, this paper presents the relations between kinetic energy and linear momentum, angular momentum of the particle and of the rigid body. The obtained results are useful for the investigation of the dynamics of multibody systems

Modeling and Simulation of Assembly in a Free-floating Work Environment by a Free-floating Robot

1996 ◽  
Vol 118 (1) ◽  
pp. 115-120 ◽  
Author(s):  
S. K. Agrawal ◽  
M. Y. Chen ◽  
M. Annapragada
Keyword(s):  
Angular Momentum ◽  
Work Environment ◽  
Multibody Systems ◽  
Rigid Body Dynamics ◽  
Analytical Models ◽  
Impact Dynamics ◽  
Dynamics Of Multibody Systems ◽  
Body Dynamics ◽  
Freely Moving ◽  
Self Motion

Freely moving systems in space conserve linear and angular momentum. As moving systems collide, the velocities get altered due to transfer of momentum. The development of strategies for assembly in a free-floating work environment requires a good understanding of primitives such as self motion of the robot, propulsion of the robot due to onboard thrusters, docking of the robot, retrieval of an object from a collection of objects, and release of an object in an object pool. The analytics of such assemblies involves not only kinematics and rigid body dynamics but also collision and impact dynamics of multibody systems. This paper presents analytical models of assembly, built from the models of primitives, and some possible strategies for overall assembly.

Modeling a Robot With Flexible Joints and Decoupling its Equations of Motion

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Flexible Joints ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Recent Advances ◽  
Dynamics Of Multibody Systems ◽  
Two Degree Of Freedom

Abstract Recent advances in the study of dynamics of multibody systems indicate the need for decoupling of the equations of motion. In this paper, our efforts are focused on this issue, and we have tried to expand the existing methods for multi-rigid body systems to include systems with some kind of flexibility. In this regard, the equations of motion for a planar two-degree-of-freedom robot with flexible joints is carried out using Lagrange’s equations and Kane’s equations with congruency transformations. The method of decoupling the equations of motion using Kane’s equations with congruency transformations is presented. Finally, the results obtained from both methods are compared.

Nonlinear Effects in Dynamic Analysis of Flexible Multibody Systems

2001 ◽  
Author(s):  
Y. C. Mbono Samba ◽  
M. Pascal
Keyword(s):  
Rigid Body ◽  
Standard Method ◽  
Multibody Systems ◽  
Nonlinear Effects ◽  
Elastic Deformations ◽  
Dynamics Of Multibody Systems ◽  
Flexible Parts ◽  
Order Of Magnitude ◽  
Rigid Body Motions ◽  
Crank Mechanism

Abstract The work is concerned with the dynamics of multibody systems with flexible parts undergoing large rigid body motions and small elastic deformations. The standard method used in most cases leads to keep only linear terms with respect to the deformations. However, for large rates or large accelerations, this linearisation is sometimes too premature. In this work, a non dimensional analysis of the system is performed, with some estimate about the order of magnitude of the different parameters occuring in the dynamical model obtained by Kane’s method [1]. A flexible slider crank mechanism is used as a test example, together with AUTOLEV [2] software for numerical results.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2005 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Application of an Angular Momentum Balance Method for Investigating Numerical Accuracy in Swirling Flow

2003 ◽  
Vol 125 (4) ◽  
pp. 723-730
Author(s):  
H. Nilsson ◽  
L. Davidson
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Angular Momentum ◽  
Swirling Flow ◽  
Linear Momentum ◽  
Correct Solution ◽  
Momentum Balance ◽  
Numerical Accuracy ◽  
Water Turbine ◽  
Water Turbines

This work derives and applies a method for the investigation of numerical accuracy in computational fluid dynamics. The method is used to investigate discretization errors in computations of swirling flow in water turbines. The work focuses on the conservation of a subset of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. However, the method can be used to investigate the effect of discretization on any equation that should be conserved in the correct solution, and the application is not limited to water turbines. Computations made for two Kaplan water turbine runners and a simplified geometry of one of the Kaplan runner ducts are investigated to highlight the general and simple applicability of the method.

scholarly journals Mass, linear momentum and kinetic energy of bipolar flows in protoplanetary nebulae

2001 ◽  
Vol 377 (3) ◽  
pp. 868-897 ◽  
Author(s):  
V. Bujarrabal ◽  
A. Castro-Carrizo ◽  
J. Alcolea ◽  
C. Sánchez Contreras
Keyword(s):  
Kinetic Energy ◽  
Linear Momentum ◽  
Protoplanetary Nebulae
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