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  • 1
    Digitale Medien
    Digitale Medien
    A computational approach for studying domains of attraction for non-linear systems
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 23 (1988), S. 279-295 
    Details
    ISSN: 0020-7462
    Quelle: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Thema: Maschinenbau , Physik
    Materialart: Digitale Medien
    URL: http://linkinghub.elsevier.com/retrieve/pii/0020-7462(88)90026-1
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  • 2
    Digitale Medien
    Digitale Medien
    Analysis of non-linear non-autonomous systems by truncated point mappings
    Amsterdam : Elsevier
    International Journal of Non-Linear Mechanics 24 (1989), S. 327-344 
    Details
    ISSN: 0020-7462
    Quelle: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Thema: Maschinenbau , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1016/0020-7462(89)90049-8
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  • 3
    Digitale Medien
    Digitale Medien
    Fitting mathematical functions to joint kinematics during stepping: Implications for motor control (1988)
    Springer
    Biological cybernetics 58 (1988), S. 91-99 
    Details
    ISSN: 1432-0770
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Informatik , Physik
    Notizen: Abstract The present study extends past work on modeling and control of stepping. The relationship between joint space kinematic data and routine motor control (i.e., open loop) during human stepping is investigated. A model of open loop stepping control using joint kinematics is described. Different functional approximations are employed to simulate experimental joint kinematic data collected on a subject stepping repeatedly over an obstacle. Results indicate that joint kinematics can be characterized by a small number of functions yielding a simple analytical description of open loop motor control. The different basis functions used and their associated coefficients reflected the qualitative behavior of joint trajectories thus allowing flexibility in the formulation of system kinematics. This approach provides a tool to study movement pathologies and movement development by identifying the basis functions governing the kinematics of motion and their associated coefficients. The model presented here is helpful in studying the segmentation of multiarticular movements into their elementary components by analytically modeling the discrete organization of motor behavior.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00364155
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  • 4
    Digitale Medien
    Digitale Medien
    Parameter optimization model of learning in stepping motion (1989)
    Springer
    Biological cybernetics 60 (1989), S. 277-284 
    Details
    ISSN: 1432-0770
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Informatik , Physik
    Notizen: Abstract In this study we combine the representation of motion by a finite number of hardwired functions with parameter optimization to model learning during a stepping motion. Representation of experimental kinematic data by a finite number of predetermined functions and undetermined coefficients was analyzed. Least squares approximation was used to represent experimental data of stepping motions over obstacles of different heights. Functional relationships between coefficients and obstacles heights were also obtained. Learning of stepping over an obstacle was then formulated as a finite dimensional optimization problem. The pattern of foot path, and joint angles trajectories obtained by this learning model, were then compared to the experimental data. The results of the data fitting analysis and of the optimization process as a model for motion learning, indicate that motion can be adequately represented by a set of hardwired functions, and a finite number of task dependent coefficients.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00204125
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  • 5
    Digitale Medien
    Digitale Medien
    Modeling of control and learning in a stepping motion (1987)
    Springer
    Biological cybernetics 55 (1987), S. 387-396 
    Details
    ISSN: 1432-0770
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Informatik , Physik
    Notizen: Abstract In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joint's motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00318373
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  • 6
    Digitale Medien
    Digitale Medien
    Phase plane modeling of leg motion (1986)
    Springer
    Biological cybernetics 53 (1986), S. 273-284 
    Details
    ISSN: 1432-0770
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Informatik , Physik
    Notizen: Abstract Phase plane analysis of dynamical systems, in which variables are plotted against their time derivatives, has been recently emphasized as a general method for reconstructing system dynamics from data. The purpose of this experiment was to develop a model of leg movement in a stepping task using the phase plane approach. In this model, the leg is represented as a three-body linkage and the motion of the leg is assumed to be planar with four degrees of freedom. Experimental data was collected on one subject stepping six times, using a two dimensional videomotion analysis system with reflective markers placed on the lower limb joints. A computer program able to solve the equations of motion and compute the state of the system for a given task was implemented. This computer program was written to generate the motion of the leg for a given task using inverse kinematics and a preplanned foot path. Foot trajectories with cycloidal, constant acceleration/deceleration and sinusoidal velocity profiles were studied. From the results, an attempt was made to identify the variables which are measured and to determine the motion characteristics during stepping. The preliminary results support the concept of a hierarchical control structure with openloop control during normal operation. During routine activity there is no direct intervention of the Central Nervous System (CNS). The results support the existence of preprogramming and provide a starting point for the study of the development of control in multiarticulate movements.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00336561
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  • 7
    Digitale Medien
    Digitale Medien
    An orthogonal decomposition approach to modal synthesis (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 471-493 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Modal synthesis is a method of formulating the equations of motion for complex vibratory systems. This approach has many advantages in modelling systems that consist of an assembly of linear dynamic elements whose modal characteristics are given. Presented in the paper is a procedure for synthesizing linear dynamic models into one dynamic description in a numerically stable way. This task is achieved by an orthogonal co-ordinate transformation replacing the matrix inversions required when other procedures are used. The modal synthesis approach is formulated as a problem of finding the equations of motion for a linear system subject to a set of linear constraints. The numerical procedure to generate the equations of motion in terms of independent co-ordinates is presented. The paper concludes with several examples that demonstrate the properties of the proposed method and its application to the modelling of vibratory systems.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620230311
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  • 8
    Digitale Medien
    Digitale Medien
    A numerical method for computing domains of attraction for dynamical systems (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 875-890 
    Details
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The backward mapping approach for computation of global domains of attraction of asymptotically stable non-critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approach.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nme.1620260409
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  • 9
    Digitale Medien
    Digitale Medien
    SPACE-TIME SPECTRAL ELEMENT METHOD FOR OPTIMAL SLEWING OF A FLEXIBLE BEAM (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3101-3121 
    Details
    ISSN: 0029-5981
    Schlagwort(e): optimal slewing ; finite elements ; flexible beam ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A new computational approach to modelling and control of a flexible beam is proposed. The structural modelling and the control design problems are formulated in a unified mathematical framework that allows simultaneous structural and control design iterations that result in an optimal overall system performance. The method employs the space-time spectral elements for simultaneous space and time discretizations of a Timoshenko beam model. Dimensionless equations of motion are derived using Hamilton's principle of variable action and an integral formulation in the framework of space-time spectral elements is introduced. An optimal control problem formulated for the continuum model is transformed by the space-time spectral element formulation into an optimization problem in a finite-dimensional parameter space. Dynamic programming is then used to obtain both open and closed loop control laws. A simulation study shows good performance of the control law applied to the nominal model. It is also demonstrated that proper discretization yields performance robustness of the system with respect to modal truncation.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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