Analytical Mechanics. 
          Foundations of Engineering Mechanics Series

Lurie, A. I.; Schiehlen, Werner

doi:10.1115/1.1641772

Cited by 9 publications

(19 citation statements)

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“…In regard to this, having costate variables λ n and κ n among them should be avoided because these quantities have a purely mathematical character and as such it is difficult to estimate their value range. In regard to this and based on (38) and (39) it is suitable to perform backward numerical integration in the interval 0, t f here. This numerical procedure consists of two steps as follows.…”

Section: The Brachistochrone Problem As An Optimal Control Problemmentioning

confidence: 99%

On the brachistochronic motion of a variable-mass mechanical system in general force fields

Obradović

Šalinić

Jeremić

et al. 2012

Mathematics and Mechanics of Solids

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The problem of the brachistochronic motion of a mechanical system composed of rigid bodies and variable-mass particles is solved. The laws of the time-rate of mass variation of the particles as well as relative velocities of the expelled (or gained) masses are assumed to be known. The system moves in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin's minimum principle along with singular optimal control theory, a corresponding two-point boundary value problem is obtained. The appropriate numerical procedure based on the shooting method to solve the obtained two-point boundary value problem is presented. The considerations in the paper are illustrated by an example of determining the brachistochronic motion of a system composed of a rigid rod and two variable-mass particles attached to the rod.

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Section: The Brachistochrone Problem As An Optimal Control Problemmentioning

confidence: 99%

On the brachistochronic motion of a variable-mass mechanical system in general force fields

Obradović

Šalinić

Jeremić

et al. 2012

Mathematics and Mechanics of Solids

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“…The parametrization of the rotation used by [17] was introduced by [21], and is very similar to one previously introduced by Darboux [22] (see also [23]). Before Romano [17] and Ivanova [24] derives a partially reduced solution for the same problem while studying the motion of a ball on a rough plate.…”

Section: Introductionmentioning

confidence: 98%

“…Furthermore, the direction of the angular momentum vector is also the direction of the angular velocity of the Virtual Sphere, because of Eq. (23). The development in this section will be exploited later in this paper for the analysis of the detumbling maneuver of an axially symmetric spacecraft.…”

Section: Case Of Constant Torque Along the Angular Momentum Vectormentioning

confidence: 99%

“…An incomplete solution for the problem in item six was previously sketched by Lurie [23]. In particular, Lurie [23] uses the Cayley-Klein's parameters in order to express the dynamics and kinematics equations as a Darboux differential equation problem, then transforms the Darboux problem into a Weber differential equation problem, which is nevertheless left unsolved.…”

Section: Introductionmentioning

confidence: 99%

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Detumbling and nutation canceling maneuvers with complete analytic reduction for axially symmetric spacecraft

Romano

2010

Acta Astronautica

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“…Historically, the relative coordinate modeling of mechanisms comprising ideal joints has been the subject of analytical mechanics, ref. to Papastavridis [124] and Lurie [92] 5.1 Configuration of a kinematic chain using the product of exponentials For illustration purpose, consider a kinematic chain with n rigid bodies interconnected by n lower pair 1-DOF joints. The central relation for the Lie group description of a serial kinematic chains is the Product-ofExponentials (POE) formula.…”

Section: Relative Coordinate Modeling Of Multibody Systems In Lie Gromentioning

confidence: 99%

Geometric methods and formulations in computational multibody system dynamics

Müller

Terze

2016

Acta Mech

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Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

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Analytical Mechanics. Foundations of Engineering Mechanics Series

Cited by 9 publications

References 0 publications

On the brachistochronic motion of a variable-mass mechanical system in general force fields

On the brachistochronic motion of a variable-mass mechanical system in general force fields

Detumbling and nutation canceling maneuvers with complete analytic reduction for axially symmetric spacecraft

Geometric methods and formulations in computational multibody system dynamics

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