The Experts below are selected from a list of 289707 Experts worldwide ranked by ideXlab platform
Yu M Zinoviev - One of the best experts on this subject based on the ideXlab platform.
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lagrangian formulation for the infinite spin n 1 supermultiplets in d 4
Nuclear Physics, 2019Co-Authors: T V Snegirev, Yu M Zinoviev, Ioseph L. Buchbinder, M V KhabarovAbstract:Abstract We provide an explicit Lagrangian construction for the massless infinite spin N = 1 supermultiplet in four dimensional Minkowski space. Such a supermultiplet contains a pair of massless bosonic and a pair of massless fermionic infinite spin fields with properly adjusted dimensionful parameters. We begin with the gauge invariant Lagrangians for such massless infinite spin bosonic and fermionic fields and derive the supertransformations which leave the sum of their Lagrangians invariant. It is shown that the algebra of these supertransformations is closed on-shell.
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gauge invariant lagrangian formulation of massive higher spin fields in a ds 3 space
Physics Letters B, 2012Co-Authors: Ioseph L. Buchbinder, T V Snegirev, Yu M ZinovievAbstract:Abstract We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional ( A ) dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
Jerrold E Marsden - One of the best experts on this subject based on the ideXlab platform.
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controlled Lagrangians and the stabilization of euler poincare mechanical systems
International Journal of Robust and Nonlinear Control, 2001Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry systems whose underlying dynamics are governed by the Euler-Poincare equations. This work extends our previous work on the stabilization of mechanical control systems using the method of controlled Lagrangians. The guiding principle behind our methodology is to develop a class of stabilizing feedback control laws which yield closed-loop dynamics that remain in Lagrangian form. Using the methodology for Euler-Poincare systems, we analyse stabilization of a satellite and an underwater vehicle controlled with momentum wheels.
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controlled Lagrangians and the stabilization of mechanical systems i the first matching theorem
IEEE Transactions on Automatic Control, 2000Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.
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stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians
International Conference on Robotics and Automation, 1999Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:Obtains feedback stabilization of an inverted pendulum on a rotor arm by the "method of controlled Lagrangians". This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or "controlled" Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy "matching" conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.
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matching and stabilization by the method of controlled Lagrangians
Conference on Decision and Control, 1998Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:We describe a class of mechanical systems for which the "method of controlled Lagrangians" provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled Lagrangian approach involves making modifications to the Lagrangian for the uncontrolled system such that the Euler-Lagrange equations derived from the modified or "controlled" Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy "matching" conditions. Our matching and stabilizability conditions are constructive; they provide the form of the controlled Lagrangian, the control law and, in some cases, conditions on the control gain(s) to ensure stability. The method is applied to stabilization of an inverted spherical pendulum on a cart and to stabilization of steady rotation of a rigid spacecraft about its unstable intermediate axis using an internal rotor.
Z E Musielak - One of the best experts on this subject based on the ideXlab platform.
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special functions of mathematical physics a unified lagrangian formalism
Mathematics, 2020Co-Authors: Z E Musielak, Niyousha Davachi, Marialis RosariofrancoAbstract:Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving the standard Lagrangians leads to Lagrangians for which the Euler–Lagrange equation vanishes identically, and that only some of these Lagrangians become the null Lagrangians with the well-defined gauge functions. It is also demonstrated that the non-standard Lagrangians require that the Euler–Lagrange equations are amended by the auxiliary conditions, which is a new phenomenon in the calculus of variations. The existence of the auxiliary conditions has profound implications on the validity of the Helmholtz conditions. The obtained results are used to derive the Lagrangians for the Airy, Bessel, Legendre and Hermite equations. The presented examples clearly demonstrate that the developed Lagrangian formalism is applicable to all considered differential equations, including the Airy (and other similar) equations, and that the regular and modified Bessel equations are the only ones with the gauge functions. Possible implications of the existence of the gauge functions for these equations are discussed.
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general conditions for the existence of non standard Lagrangians for dissipative dynamical systems
Chaos Solitons & Fractals, 2009Co-Authors: Z E MusielakAbstract:Abstract Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangians and derive equations of motion resulting from these Lagrangians.
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standard and non standard Lagrangians for dissipative dynamical systems with variable coefficients
Journal of Physics A, 2008Co-Authors: Z E MusielakAbstract:Dynamical systems described by equations of motion with the first-order time derivative (dissipative) terms of even and odd powers, and coefficients varying either in time or in space, are considered. Methods to obtain standard and non-standard Lagrangians are presented and used to identify classes of equations of motion that admit a Lagrangian description. It is shown that there are two general classes of equations that have standard Lagrangians and one special class of equations that can only be derived from non-standard Lagrangians. In addition, each general class has a subset of equations with non-standard Lagrangians. Conditions required for the existence of standard and non-standard Lagrangians are derived and a relationship between these two types of Lagrangians is introduced. By obtaining Lagrangians for several dynamical systems and some basic equations of mathematical physics, it is demonstrated that the presented methods can be applied to a broad range of physical problems.
Jorge Zanelli - One of the best experts on this subject based on the ideXlab platform.
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higher dimensional gravity propagating torsion and ads gauge invariance
Classical and Quantum Gravity, 2000Co-Authors: Ricardo Troncoso, Jorge ZanelliAbstract:The most general theory of gravity in d dimensions which leads to second-order field equations for the metric has [(d-1)/2] free parameters. It is shown that requiring the theory to have the maximum possible number of degrees of freedom, fixes these parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern-Simons form for the (A)dS or Poincare groups. In even dimensions, the action has a Born-Infeld-like form. Torsion may occur explicitly in the Lagrangian in the odd-parity sector and the torsional pieces respect local (A)dS symmetry for d = 4k-1 only. These torsional Lagrangians are related to the Chern-Pontryagin characters for the (A)dS group. The additional coefficients in front of these new terms in the Lagrangian are shown to be quantized.
Anthony M Bloch - One of the best experts on this subject based on the ideXlab platform.
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controlled Lagrangians and the stabilization of euler poincare mechanical systems
International Journal of Robust and Nonlinear Control, 2001Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:In this paper we develop a constructive approach to the determination of stabilizing control laws for a class of Lagrangian mechanical systems with symmetry systems whose underlying dynamics are governed by the Euler-Poincare equations. This work extends our previous work on the stabilization of mechanical control systems using the method of controlled Lagrangians. The guiding principle behind our methodology is to develop a class of stabilizing feedback control laws which yield closed-loop dynamics that remain in Lagrangian form. Using the methodology for Euler-Poincare systems, we analyse stabilization of a satellite and an underwater vehicle controlled with momentum wheels.
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controlled Lagrangians and the stabilization of mechanical systems i the first matching theorem
IEEE Transactions on Automatic Control, 2000Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.
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stabilization of the pendulum on a rotor arm by the method of controlled Lagrangians
International Conference on Robotics and Automation, 1999Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:Obtains feedback stabilization of an inverted pendulum on a rotor arm by the "method of controlled Lagrangians". This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or "controlled" Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy "matching" conditions. The pendulum on a rotor arm requires an interesting generalization of our earlier approach which was used for systems such as a pendulum on a cart.
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matching and stabilization by the method of controlled Lagrangians
Conference on Decision and Control, 1998Co-Authors: Anthony M Bloch, Naomi Ehrich Leonard, Jerrold E MarsdenAbstract:We describe a class of mechanical systems for which the "method of controlled Lagrangians" provides a family of control laws that stabilize an unstable (relative) equilibrium. The controlled Lagrangian approach involves making modifications to the Lagrangian for the uncontrolled system such that the Euler-Lagrange equations derived from the modified or "controlled" Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inputs, the modifications to the Lagrangian must satisfy "matching" conditions. Our matching and stabilizability conditions are constructive; they provide the form of the controlled Lagrangian, the control law and, in some cases, conditions on the control gain(s) to ensure stability. The method is applied to stabilization of an inverted spherical pendulum on a cart and to stabilization of steady rotation of a rigid spacecraft about its unstable intermediate axis using an internal rotor.
