ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
Collection
Publisher
Years
  • 1
    facet.materialart.
    Unknown
    Variational multirate integration of constrained dynamics (2012)
    Wiley
    Details
    Publication Date: 2012-04-18
    Description: Mechanical systems with dynamics on varying time scales, in particular those including highly oscillatory motion, impose challenging questions for numerical integration schemes. Tiny step sizes are required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a larger time step is accurate enough. Small time steps increase integration times unnecessarily, especially for costly function evaluations. For systems comprising fast and slow dynamics, multirate methods integrate the slow part of the system with a relatively large step size while the fast part is integrated with a small time step. Main challenges are the identification of fast and slow parts (e.g. by separating the energy or by distinguishing sets of variables), the synchronisation of their dynamics and in particular the treatment of mixed parts that often appear when fast and slow dynamics are coupled by constraints. In this contribution, a multirate integrator is derived in closed form via a discrete variational principle on a time grid consisting of macro and micro time nodes. Variational integrators (based on a discrete version of Hamilton's principle) lead to symplectic and momentum preserving integration schemes that also exhibit good energy behavior. The resulting multirate variational integrator has the same preservation properties. An example demonstrates the performance of the multirate integrator for constrained multibody dynamics. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 2
    facet.materialart.
    Unknown
    Variational multirate integration of constrained dynamics (2011)
    Wiley
    Details
    Publication Date: 2011-12-10
    Description: Mechanical systems with dynamics on varying time scales, in particular those including highly oscillatory motion, impose challenging questions for numerical integration schemes. Tiny step sizes are required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a larger time step is accurate enough. Small time steps increase integration times unnecessarily, especially for costly function evaluations. For systems comprising fast and slow dynamics, multirate methods integrate the slow part of the system with a relatively large step size while the fast part is integrated with a small time step. Main challenges are the identification of fast and slow parts (e.g. by separating the energy or by distinguishing sets of variables), the synchronisation of their dynamics and in particular the treatment of mixed parts that often appear when fast and slow dynamics are coupled by constraints. In this contribution, a multirate integrator is derived in closed form via a discrete variational principle on a time grid consisting of macro and micro time nodes. Variational integrators (based on a discrete version of Hamilton's principle) lead to symplectic and momentum preserving integration schemes that also exhibit good energy behavior. The resulting multirate variational integrator has the same preservation properties. An example demonstrates the performance of the multirate integrator for constrained multibody dynamics. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 3
    facet.materialart.
    Unknown
    Limitations of computing time savings in variational multirate integrations (2014)
    Wiley
    Details
    Publication Date: 2014-12-23
    Description: For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using a time grid consisting of micro and macro nodes. This leads to computing time savings, however not unlimited, for a certain number of micro steps per macro step the computing time is minimal. To find a relation between this minimum computing time and the number of variables in the system, the computing time for the Fermi-Pasta-Ulam problem (FPU) is measured for different numbers of masses and different numbers of micro steps. In addition, the numerical convergence of the variational multirate integration is shown for the FPU. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 4
    facet.materialart.
    Unknown
    Variational multirate integration in multi-body dynamics (2016)
    Wiley
    Details
    Publication Date: 2016-10-26
    Description: For systems that contain slow and fast dynamics, variational multirate integration schemes are used. These schemes split the system into parts which are simulated using two time grids consisting of micro and macro nodes. This formulation can be extended for multi-body systems. The rigid multi-body system is described by the so called director formulation and constraints describing the joints connecting the bodies. With the Lagrange multiplier method, the constraints are introduced into the equations of motion. A way to implement the null space method into the variational multirate framework is shown and the influence on the number of unknowns is investigated. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 5
    facet.materialart.
    Unknown
    Multiobjective optimal control of a four-body kinematic chain (2013)
    Wiley
    Details
    Publication Date: 2013-11-30
    Description: Optimal control of mechanical systems is an active area of research. However, so far, most contributions are taking only one single objective into account, whereas for many practical problems, one is interested in optimizing several conflicting objectives at the same time. Applying singleobjective optimization to each of them leads to several trajectories each being optimal for one objective, but ignoring all others. In contrast to that, combining all objectives and using multiobjective optimization leads to a variety of trade off solutions taking all objectives into account simultaneously. We use the direct discretization method DMOCC (Discrete Mechanics and Optimal Control for Constrained systems) to approximate trajectories of the underlying optimal control problems, resulting in restricted optimization problems of high dimension. For the multiobjective part, we apply a reference point technique which successively utilizes an auxiliary distance function to gain the trade off solutions. The presented approach is illustrated by the multiobjective optimal control of a constrained multibody system. A four-body kinematic chain is controlled in a rest to rest maneuver, for which minimal control effort and minimal required maneuver time are the conflicting objectives. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 6
    facet.materialart.
    Unknown
    Computing time investigations for variational multirate integration (2013)
    Wiley
    Details
    Publication Date: 2013-11-30
    Description: Consider a mechanical system that contains slow and fast dynamics. Let it be possible, to split the potential energy into a slow and a fast potential and the configuration vector into slow and fast variables. For such systems, multirate schemes simulate the different parts using different time steps with the goal to save computing time. For the proposed multirate scheme, a time grid consisting of micro and macro nodes is used and the integrator is derived from a discrete variational principle. Variational integrators conserve properties like symplecticity and momentum maps and have good energy behavior. To solve the resulting system of coupled nonlinear equations, a Newton-Raphson iteration with an analytical Jacobian is used. It is demonstrated that the multirate approach leads to less computing time compared to singlerate simulation by means of three example systems, the Fermi-Pasta-Ulam problem, a triple spherical pendulum and a simple atomistic model, where the latter two are subject to constraints. Computing times are compared for different numbers of micro and macro nodes for dynamic simulations during a certain time interval. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
  • 7
    facet.materialart.
    Unknown
    Asynchronous variational Lie group integration for geometrically exact beam dynamics (2013)
    Wiley
    Details
    Publication Date: 2013-11-30
    Description: For the elastodynamic simulation of a spatially discretized beam, asynchronous variational integrators (AVI) offer the possibility to use different time steps for every element [1]. They are symplectic and conserve discrete momentum maps and since the presented integrator for geometrically exact beam dynamics [2] is derived in the Lie group setting ( SO (3) for the representation of rotational degrees of freedom), it intrinsically preserves the group structure without the need for constraints [3]. A decrease of computational cost is to be expected in situations, where the time steps have to be very low in certain parts of the beam but not everywhere, e.g. if some regions of the beam are moving faster than others. The implementation allows synchronous as well as asynchronous time stepping and shows very good energy behaviour, i.e. there is no drift of the total energy for conservative systems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Electronic ISSN: 1617-7061
    Topics: Mathematics , Physics , Technology
    Published by Wiley
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    PAPER CURRENT
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...