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Hamilton's Principle (hamilton + principle)
Selected AbstractsVibration of a porouse-cellular circular platePROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Ewa Magnucka-Blandzi The subject of investigation is a circular porous-cellular plate under uniform pressure. Mechanical properties of the isotropic porous cellular metal vary accross the thickness of the plate. Middle plane of the plate is its symmetry plane. Fields of diseplacements and stresses with respect the nonlinear hypothesis are described. Basing on Hamilton principle three motion equations of the plate are formulated. These equations are approximately solved. The vibration problem is reduced to the second-order differential equation. Numerical investigations are realised for family of plates. Natural frequencies are determined. The obtained results are shown in Figures. To the end of the investigation comparition analyses with respect to homogeneous plates is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] PECTIVE: HERE'S TO FISHER, ADDITIVE GENETIC VARIANCE, AND THE FUNDAMENTALTHEOREM OF NATURAL SELECTIONEVOLUTION, Issue 7 2002James F. Crow Abstract Fisher's fundamental theorem of natural selection, that the rate of change of fitness is given by the additive genetic variance of fitness, has generated much discussion since its appearance in 1930. Fisher tried to capture in the formula the change in population fitness attributable to changes of allele frequencies, when all else is not included. Lessar's formulation comes closest to Fisher's intention, as well as this can be judged. Additional terms can be added to account for other changes. The "theorem" as stated by Fisher is not exact, and therefore not a theorem, but it does encapsulate a great deal of evolutionary meaning in a simple statement. I also discuss the effectiveness of reproductive-value weighting and the theorem in integrated form. Finally, an optimum principle, analogous to least action and Hamilton's principle in physics, is discussed. [source] Vertical dynamic responses of a simply supported bridge subjected to a moving train with two-wheelset vehicles using modal analysis methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2005Ping Lou Abstract The vertical dynamic responses of a simply supported bridge subjected to a moving train are investigated by means of the modal analysis method. Each vehicle of train is modelled as a four-degree-of-freedom mass,spring,damper multi-rigid body system with a car body and two wheelsets. The bridge, together with track, is modelled as a simply supported Bernoulli,Euler beam. The deflection of the beam is described by superimposing modes. The train and the beam are regarded as an entire dynamic system, in which the contact forces between wheelset and beam are considered as internal forces. The equations of vertical motion in matrix form with time-dependent coefficients for this system are directly derived from the Hamilton's principle. The equations of motion are solved by Wilson-, method to obtain the dynamic responses for both the support beam and the moving train. Compared with the results previous reported, good agreement between the proposed method and the finite element method is obtained. Finally, the effects of beam mode number, vehicle number, beam top surface, and train velocity on the dynamic responses of the entire train and bridge coupling system are studied, and the dynamic responses of beam are given under the train moving with resonant velocity. Copyright © 2005 John Wiley & Sons, Ltd. [source] Manoeuvring and vibration reduction of a flexible spacecraft integrating optimal sliding mode controller and distributed piezoelectric sensors/actuatorsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 6 2007Qinglei Hu Abstract This investigation is to apply optimal sliding mode (OSM) control theory and distributed piezoelectric sensor/actuator technology to vibration control of a flexible spacecraft. An approximate analytical dynamic model of a slewing flexible spacecraft with surface-bonded piezoelectric sensors/actuators is developed using Hamilton's principle with discretization by assumed model method. To satisfy pointing requirements and simultaneously suppress vibration, two separate control loops are adopted. The first uses the piezoceramics as sensors and actuators to actively suppress certain flexible modes by designing a positive position feedback (PPF) compensators that add damping to the flexible structures in certain critical modes in the inner feedback loop; then a second feedback loop is designed using OSM control to slew the spacecraft. The OSM controller minimizes the expected value of a quadratic objective function consisting of only the states with the constraints that the error states always remain on the intersection of sliding surfaces. The advantage in this method is that the vibration reduction and attitude control are achieved separately in the two separate feedback loops, allowing the pointing requirements and simultaneous vibrations suppression to be satisfied independently of one another. An additional attraction of the design method is that the selection of PPF gain is determined by introducing a cost function to be minimized by the feedback gains which are subject to the stability criterion at the same time, such that the feedback gains are selected in a more systematical way to avoid the arbitrary selecting of feedback gains. The proposed control strategy has been implemented on a flexible spacecraft, which is a hub with a cantilever flexible beam appendage and can undergo a single axis rotation. Both analytical and numerical results are presented to show the theoretical and practical merits of this approach. Copyright © 2006 John Wiley & Sons, Ltd. [source] Robust force control of a flexible arm with a nonsymmetric rigid tip bodyJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 5 2001Yoshifumi Morita In this article, we discuss modeling and robust control of bending and torsional vibrations and contact force of a flexible arm with a nonsymmetric rigid tip body. By using Hamilton's principle and the Lagrange multiplier method, dynamic equations of the constrained flexible arm are derived. Since the flexible arm has the nonsymmetric tip body, the bending and torsional vibrations are coupled. As the obtained boundary conditions of the distributed parameter system are nonhomogeneous, we introduce a change of variables to derive homogeneous boundary conditions. By using the eigenvalues and the correpsonding eigenfunctions related to the distributed parameter system, we derive a finite-dimensional modal model. To compensate for the spillover instability, we construct robust controllers of an optimal controller with a low-pass property and an H, controller. Some experiments have been carried out to show the effectiveness of the proposed robust controllers. © 2001 John Wiley & Sons, Inc. [source] A Note on a Nonlinear Model of a Piezoelectric RodPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003R. Gausmann Dipl.-Ing. If piezoceramics are excited by weak electric fields a nonlinear behavior can be observed, if the excitation frequency is close to a resonance frequency of the system. To derive a theoretical model nonlinear constitutive equations are used, to describe the longitudinal oscillations of a slender piezoceramic rod near the first resonance frequency. Hamilton's principle is used to receive a variational principle for the piezoelectric rod. Introducing a Rayleigh Ritz ansatz with the eigenfunctions of the linearized system to approximate the exact solution leads to nonlinear ordinary differential equations. These equations are approximated with the method of harmonic balance. Finally it is possible to calculate the amplitudes of the displacements numerically. As a result it is shown, that the Duffing type nonlinearities found in measurements can be described with this model. [source] Force/motion sliding mode control of three typical mechanismsASIAN JOURNAL OF CONTROL, Issue 2 2009Rong-Fong Fung Abstract This paper proposes a sliding mode control (SMC) algorithm for trajectory tracking of the slider-crank mechanism, quick-return mechanism, and toggle mechanism. First, the dynamic models suitable for the controls of both the motion and constrained force are derived using Hamilton's principle, the Lagrange multiplier, and implicit function theory. Second, the SMC is designed to ensure the input torques can achieve trajectory tracking on the constrained surfaces with specific constraint forces. Finally, the developed method is successfully verified for effectiveness of the force/motion controls for these three typical mechanisms from the results of simulation. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] Planar distribution of the galaxies in the Local GroupASTRONOMISCHE NACHRICHTEN, Issue 9-10 2008S. Pasetto Abstract Adopting known data on positions and distances, we make use of analytical geometry and look for the plane that minimizes the distances of all galaxies to it. A planar distribution is found. We apply Hamilton's principle of minimum action to investigate the dynamics of the two major systems of the Local Group, the Milky Way and Andromeda, under the action of forces exerted by nearby galaxies or groups external to the Local Group. We find that the planar distribution is fully compatible with the minimum action and that the external force field is likely parallel to the plane. It pulls the galaxies of the Local Group without altering their planar distribution. Special care is paid to evaluate the robustness of this result. We present an explanation in the linear regime of the numerical results based on the compression effect described with the tidal tensor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||