existence of a class of rotopulsators abstract we prove the existence of a class of rotopulsators for the n body problem in spaces of constant gaussian curvature of dimension k 2

rotopulsators of the curved n body problem we consider the n body problem in spaces of constant curvature and study its rotopulsators i e solutions for which the configuration of the bodies rotates and changes size during the motion rotopulsators fall naturally into five groups positive elliptic positive elliptic elliptic negative elliptic negative hyperbolic and negative elliptic hyperbolic depending on the nature and number of their rotations and on whether they occur in spaces of positive or negative curvature after obtaining existence criteria for each type of rotopulsator we derive their conservation laws we further deal with the existence and uniqueness of some classes of rotopulsators in the 2 and 3 body case and prove two general results about the qualitative behaviour of rotopulsators more precisely for positive curvature we show that there is no foliation of the 3 sphere with clifford tori such that the motion of each body is confined to some clifford torus for negative curvature a similar result is proved relative to foliations of the hyperbolic 3 sphere with hyperbolic cylinders

polygonal homographic orbits of the curved n body problem in the 2 dimensional n body problem n 3 in spaces of constant curvature 6 0 we study polygonal homographic solutions we first provide necessary and sufficient conditions for the existence of these orbits and then consider the case of regular polygons we further use this criterion to show that for any n 3 the regular ngon is a polygonal homographic orbit if and only if all masses are equal then we prove the existence of relative equilibria of non equal masses on the sphere of curvature 0 for n 3 in the case of scalene triangles such triangular relative equilibria occur only along fixed geodesics and are generated from fixed points of the sphere finally through a classification of the isosceles case we prove that not any three masses can form a triangular relative equilibrium

cross sectional analysis of nonhomogeneous anisotropic active slender structures a general formulation for the reduction of the three dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented the dimensional reduction is based on a variationalasymptotic formulation using the slenderness ratio as small parameter in the proposed scheme the coupled linear electroelastic equations are solved at the cross sectional level using the finite element method furthermore modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis and arbitrary electric modes are used to define applied electric fields at the cross section this results in a general definition of a coupled electroelastic stiffness which can be used in virtually all composite and active beam formulations as well as in the development of new low order high accuracy reduced models for active structures finally the formulation also yields recovery relations for the elastic and electric fields in the original three dimensional solid once the one dimensional problem is solved the method has been implemented in a computer program um vabs and numerical results are presented for active anisotropic beam cross sections of simple geometries which are shown to compare very well with three dimensional finite element analysis

existence of a lower bound for the distance between point masses of relative equilibria in spaces of constant curvature abstract we prove that if for the curved n body problem the masses are given the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero we furthermore prove that the set of all such relative equilibria is compact this class of relative equilibria includes all relative equilibria of the curved n body problem in h 2 and a significant subset of the relative equilibria for s 2 s 3 and h 3

a new galerkin based approach for accurate non linear normal modes through invariant manifolds a method for producing accurate reduced order models of non linear vibratory systems is presented based on the invariant manifold description of non linear normal modes nnm this approach makes use of polar co ordinates to obtain equations which govern the geometry of the invariant manifold these equations are discretized through a series expansion and galerkin projection over a chosen amplitude and phase domain yielding non linear equations in the expansion coefficients these equations when solved numerically yield an invariant manifold which is accurate to the degree of the expansion and devoid of the limitations which plague typical asymptotic solutions such galerkin based solutions may be used to generate accurate reduced order models for large amplitude strongly non linear motions this procedure is illustrated using two non linear examples a two degree of freedom oscillator and a finite element beam model the solution convergence and manifold geometry are discussed and the resultant reduced order models are shown to possess exceptional accuracy over large amplitude ranges this approach allows the full potential of the invariant manifold formulation to be reached and is suitably general for application to a wide variety of non linear systems

boundary controllability of sobolev type abstract nonlinear integrodifferential systems sufficient conditions are established for boundary controllability of various classes of sobolev type nonlinear systems including integrodifferential systems in banach spaces the results are obtained using the strongly continuous semigroup of operators and the banach contraction principle examples are provided to illustrate the theory

nonlinear normal modes in an intrinsic theory of anisotropic beams nonlinear normal modes in nonlinear oscillations of beams are derived from intrinsic equations that is using velocities and strains as primary degrees of freedom displacements and rotations are thus not system states but are instead obtained using the propagation of the local beam material reference frames as in rigid body dynamics it is shown that the intrinsic variables sufce to describe the free vibrations of the beam the approach does not need assumptions in the material properties i e it is valid for general anisotropic behavior or the beam kinematics i e it is based on cosserat s exact geometrical description of the deformable curve furthermore the nonlinear modal equations in intrinsic coordinates are obtained from integrals involving only products of the mode shapes and known coecients using this

boundary controllability of differential equations with nonlocal condition for a semilinear boundary control system with a nonlocal condition using a banach fixed point theorem we prove the boundary controllable and we give an application

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

a new formulation for the existence and calculation of nonlinear normal modes a new formulation is presented here for the existence and calculation of nonlinear normal modes in undamped nonlinear autonomous mechanical systems as in the linear case an expression is developed for the mode in terms of the amplitude mode shape and frequency with the distinctive feature that the last two quantities are amplitude and total phase dependent the dynamic of the periodic response is defined by a one dimensional nonlinear differential equation governing the total phase motion the period of the oscillations depending only on the amplitude is easily deduced it is established that the frequency and the mode shape provide the solution to a 2 periodic nonlinear eigenvalue problem from which a numerical galerkin procedure is developed for approximating the nonlinear modes the procedure is applied to various mechanical systems with two degrees of freedom

on the singularities of the curved n body problem we study singularities of the n body problem in spaces of constant curvature and generalize certain results due to painleve weierstrass and sundman for positive curvature some of our proofs use the correspondence between total collision solutions of the original system and their orthogonal projection a property that offers a new method of approaching the problem in this par ticular case

normal modes of vibration for non linear continuous systems a definition and a constructive methodology for normal nodes of motion are developed for a class of vibratory systems the dynamics of which are governed by non linear partial differential equations the definition for normal modes is given in terms of the dynamics on two dimensional invariant manifolds in the system phase space these manifolds are a continuation of the planes which represent the well known normal modes of the linearized system a local asymptotic approximation of the geometric structure of these manifolds can be obtained by using an approach which follows that used for generating center manifolds the procedure also provides the non linear ordinary differential equations which govern individual modal dynamics and a physical description of the system configuration when it is undergoing a modal motion in this paper the general theory is described for the application of vibrations of continuous media but it can easily be extended to other situations in order to demonstrate the power of the approach and its unique procedural aspects three examples involving beam vibrations are worked out in detail the examples are conservative simply supported beams the first demonstrates the methodology for a linear beam model the second is a beam on a non linear elastic foundation and the third example is a beam with non linear torsional springs attached at each end in these examples the simplicity of the mode shapes of the linearized model yields relatively simple calculations that do not obscure the important features of the procedure

existence and controllability results for impulsive partial functional differential inclusions abstract in this paper we prove the existence and the controllability of mild and extremal mild solutions for first order semilinear densely defined impulsive functional differential inclusions in separable banach spaces with local and nonlocal conditions

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

periodic solutions for some nonautonomous semilinear boundary evolution equations abstract in this work we study the massera problem for the existence of a periodic mild solution of a class of nonautonomous semilinear boundary evolution equations 0 1 x t a m t x t f t x t t 0 l t x t t x t g t x t t 0 x 0 x 0 first we prove the existence of a periodic solution for nonhomogeneous boundary evolution equations under the existence of a bounded solution on the right half real line next by using a fixed point theorem we investigate the existence of periodic solutions in the semilinear case we end with an application to a periodic heat equation with semilinear boundary conditions

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

geometrically exact intrinsic theory for dynamics of curved and twisted anisotropic beams a formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams when the applied loads at the ends of and distributed along the beam are independent of the deformation neither displacement nor rotation variables appear an intrinsic formulation like well known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two advantages of such a formulation are demonstrated with a simple example when the initial curvature and twist are constant along the beam two space time conservation laws are shown to exist one being a work energy relation and the other a generalized impulse momentum relation these laws can be used for example as benchmarks to check the accuracy of any proposed solution including time marching and finite element schemes the structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization a particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end loaded beams that by virtue of the kirchhoff analogy leads to a time marching scheme for the dynamics of a pivoted rigid body in a gravity field this time marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy whereas the analogous spatial discretization scheme for the nonlinear static behavior of end loaded beams satisfies analogous integrals of deformation along the beam span remarkably a straightforward generalization of these discretization schemes is shown to satisfy both space time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space time element

polygonal rotopulsators of the curved n body problem we revisit polygonal positive elliptic rotopulsator solutions and polygonal negative elliptic rotopulsator solutions of the n body problem in h3 and s3 and prove the existence of these solutions and prove that the masses of these rotopulsators have to be equal if the rotopulsators are of nonconstant size and show that the number of negative elliptic relative equilibria of this type is finite as is the number of positive elliptic relative equilibria if an upper bound on the size of the relative equilibrium is imposed additionally we prove that a class of negative hyperbolic rotopulsators is in fact a subclass of the class of polygonal negative elliptic rotopulsators

nonlinear normal modes of structural systems via asymptotic approach abstract an asymptotic approach based on the method of multiple scales is employed to construct the nonlinear normal modes nnm s of self adjoint structural systems with arbitrary linear inertia and elastic stiffness operators general cubic inertia and geometric nonlinearities the methodology employed for constructing the approximate invariant manifolds of individual nnm s away from internal resonances and of the resonant modes near three to one internal resonances attempts to generalize previous studies based on asymptotic techniques the theory is applied to a hinged hinged uniform elastic beam carrying a lumped mass and undergoing axis stretching depending on the lumped mass relative to the beam mass and on its position along the span different classes of nonlinear normal modes and their stability are investigated

controllability of semilinear boundary problems with nonlocal initial conditions the main purpose of this paper is the existence of solutions and controllability for semilinear boundary problems with nonlocal initial conditions we show that the solutions are given by a variation of constants formula which allows us to study the exact controllability for this kind of problems with control and nonlinear terms at the boundary the included application to a size structured population equation provides a motivation for abstract results

finiteness of polygonal relative equilibria for generalised quasi homogeneous n body problems and n body problems in spaces of constant curvature we prove for generalisations of quasi homogeneous n body problems with centre of mass zero and n body problems in spaces of negative constant gaussian curvature that if the masses and rotation are fixed there exists for every order of the masses at most one equivalence class of relative equilibria for which the point masses lie on a circle as well as that there exists for every order of the masses at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass the method of proof is a generalised version of a proof by j m cors g r hall and g e roberts on the uniqueness of co circular central configurations for power law potentials

controllability of evolution differential inclusions in banach spaces abstract in this paper we consider the controllability of a certain class of evolution differential inclusions in banach spaces a sufficient condition is established by using a recent fixed point theorem for multi valued maps due to dhage combined with an evolution system an example is also given to illustrate our result

geometrically nonlinear flexural vibrations of plates in plane boundary conditions and some symmetry properties abstract this study is devoted to the derivation of some properties of the von karman equations for geometrically nonlinear models of plates with a boundary of arbitrary shape for applications to nonlinear vibration and buckling an intrinsic formulation of the local partial differential equations in terms of the transverse displacement and an airy stress function as unknowns is provided classical homogeneous boundary conditions with vanishing prescribed forces and displacements are derived in terms of the airy stress function in the case of a boundary of arbitrary geometry a special property of this operator crucial for some energy conserving numerical schemes and called triple self adjointness is derived in the case of an edge of arbitrary shape it is shown that this property takes a simple form for some classical boundary conditions so that the calculations in some practical cases are also simplified the applications of this work are either semi analytical methods of solution using an expansion of the solution onto an eigenmode basis of the associated linear problem or special energy conserving numerical methods

dynamic response of intrinsic continua for use in biological and molecular modeling explicit finite element formulation an intrinsic beam formulation has recently appeared aiaa j 2003 41 6 1131 1137 which presents the three dimensional equations of motion governing spatial and temporal changes in a one dimensional continua s curvature strain rectilinear velocity and angular velocity the formulation would suggest several computational advantages over more traditional displacement based continua approaches low order interpolation functions can describe generally curved and twisted continua configurations inter element displacements slopes strains and curvatures can be matched and finite rotational variables and their complexities are absent here we present a completed intrinsic continua finite element development and critical analysis which follows from an earlier preliminary treatment as applied to carbon nanotubes int j solids struct 2007 44 874 894 modeling of nodal displacements and rotations are included explicit time stepping with desired high frequency damping is accomplished using an implementation of the generalized method zero energy modes inherent in the formulation are also identified and rectified finally we document very good agreement between results predicted with the intrinsic continua finite element simulator and results generated using more traditional finite element simulations copyright 2009 john wiley sons ltd

controllability of evolution inclusions with nonlocal conditions in this paper we examine controllability problems of evolution inclusions with nonlocal conditions using kakutani s fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

controllability of sobolev type integrodifferential systems in banach spaces sufficient conditions for controllability of sobolev type integrodifferential systems in banach spaces are established the results are obtained using compact semigroups and the schauder fixed point theorem as an example is provided to illustrate the results

existence of a lower bound for the distance between point masses of relative equilibria for generalised quasi homogeneous n body problems and the curved n body problem we prove that if for relative equilibrium solutions of a generalisation of quasi homogeneous n body problems the masses and rotation are given then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero we furthermore prove that the set of such relative equilibria is compact and prove related results for n body problems in spaces of constant gaussian curvature

an energy preserving description of nonlinear beam vibrations in modal coordinates abstract conserved quantities are identified in the equations describing large amplitude free vibrations of beams projected onto their linear normal modes this is achieved by writing the geometrically exact equations of motion in their intrinsic or hamiltonian form before the modal transformation for nonlinear free vibrations about a zero force equilibrium it is shown that the finite dimensional equations of motion in modal coordinates are energy preserving even though they only approximate the total energy of the infinite dimensional system for beams with constant follower forces energy like conserved quantities are also obtained in the finite dimensional equations of motion via casimir functions the duality between space and time variables in the intrinsic description is finally carried over to the definition of a conserved quantity in space which is identified as the local cross sectional power numerical examples are used to illustrate the main results

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

boundary control problems with nonlinear state equation first order necessary conditions of optimality are obtained for boundary control problems governed by parabolic equations with nonlinear boundary value conditions

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli