Formulation of Equations of Motion for Complex Spacecraft

An engineering approach to the dynamic control of space robotic on-orbit servicers

“…However, the NE method remains 60 per cent more efficient than the recursive LE method, and for this reason was adopted for dynamic simulation of all Canadian space manipulators. Several dynamic formulations for multi-body space systems have been subject to comparison, and these analyses conclude that recursive NE methods are much more efficient computationally than LE approaches [27], a conclusion reiterated in its application to space-based manipulators [28]. A derivative method of the NE technique-Kane's equations-numerically linearizes the kinematics to give generalized velocities and enables the derivation of generalized forces by serial approximation [27].…”

“…Several dynamic formulations for multi-body space systems have been subject to comparison, and these analyses conclude that recursive NE methods are much more efficient computationally than LE approaches [27], a conclusion reiterated in its application to space-based manipulators [28]. A derivative method of the NE technique-Kane's equations-numerically linearizes the kinematics to give generalized velocities and enables the derivation of generalized forces by serial approximation [27]. These equations were adapted specifically for robotics applications [29] which formed the basis of an approach to the analysis of a two-armed space robot [30].…”

Multi flexible body analysis for application to wind turbine control design

“…The methodology is based on breaking a generic, 2-bladed, teetering-rotor HAWT into flexible and multi-rigid-body subsystems Specifically because of the intended use of the code, the analysis is tailored to minimize the complexity associated with the multi-rigid-body part of the system, which is accomplished by using Kane's method [7]. This is known to lead to simpler equations of motion than conventional methods [8]. Simultaneously, the methodology must provide the needed fidelity for the flexible elements.…”

A simple rigid body algorithm for structural dynamics programs

“…Denoting the kinetic energy at a point, written in terms of the quasi-co-ordinates and the generalized displacements, as T*, the weak form of Lagrange's equation is derived by substituting equations (13) and (14) in equation (11): where F is the deformation gradient a x i / d X j , and 6F is (axi/dqk)6qk,j. The classical form of the Boltzmann-Hamel equation corresponds to the virtual power instead of the virtual work weak form:…”