A treatise upon analytical mechanics : being the first book of the Mécanique céleste /

On spine: Laplace's mechanics.

Analytical mechanics for engineers,

Mode of access: Internet.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

Canonical formalism for path dependent Lagrangians. Coupling constant expansions

A canonical formalism obtained for path-dependent Lagrangians is applied to Fokker-type Lagrangians. The results are specialized for coupling constant expansions and later on are applied to relativistic systems of particles interacting through symmetric scalar and vector mesodynamics and electrodynamics.

Um esboço da história do conceito de trabalho virtual e suas aplicações

Neste trabalho abordamos a questão concernente à origem do princípio de trabalho virtual e sua consolidação como um dos conceitos fundamentais no estudo da mecânica analítica e, em particular, dos sistemas em equilíbrio estático. Ênfase foi dada às contribuições seminais de Stevin, Galileu e, sobretudo, as de d'Alembert e Lagrange, no tocante ao conceito de trabalho virtual. Além disso, faz-se um comentário geral sobre vínculos holônomos e deslocamento virtual. Alguns exemplos de emprego da equação de d'Alembert-Lagrange são apresentados, para mostrar como o princípio de trabalho virtual pode ser adequadamente aplicado.

A contribution for developing more efficient dynamic modelling algorithms of parallel robots

Parallel kinematic structures are considered very adequate architectures for positioning and orienti ng the tools of robotic mechanisms. However, developing dynamic models for this kind of systems is sometimes a difficult task. In fact, the direct application of traditional methods of robotics, for modelling and analysing such systems, usually does not lead to efficient and systematic algorithms. This work addre sses this issue: to present a modular approach to generate the dynamic model and through some convenient modifications, how we can make these methods more applicable to parallel structures as well. Kane’s formulati on to obtain the dynamic equations is shown to be one of the easiest ways to deal with redundant coordinates and kinematic constraints, so that a suitable c hoice of a set of coordinates allows the remaining of the modelling procedure to be computer aided. The advantages of this approach are discussed in the modelling of a 3-dof parallel asymmetric mechanisms.

A contribution on modeling methodologies for multibody systems.

Multibody System Dynamics has been responsible for revolutionizing Mechanical Engineering Design by using mathematical models to simulate and optimize the dynamic behavior of a wide range of mechanical systems. These mathematical models not only can provide valuable informations about a system that could otherwise be obtained only by experiments with prototypes, but also have been responsible for the development of many model-based control systems. This work represents a contribution for dynamic modeling of multibody mechanical systems by developing a novel recursive modular methodology that unifies the main contributions of several Classical Mechanics formalisms. The reason for proposing such a methodology is to motivate the implementation of computational routines for modeling complex multibody mechanical systems without being dependent on closed source software and, consequently, to contribute for the teaching of Multibody System Dynamics in undergraduate and graduate levels. All the theoretical developments are based on and motivated by a critical literature review, leading to a general matrix form of the dynamic equations of motion of a multibody mechanical system (that can be expressed in terms of any set of variables adopted for the description of motions performed by the system, even if such a set includes redundant variables) and to a general recursive methodology for obtaining mathematical models of complex systems given a set of equations describing the dynamics of each of its uncoupled subsystems and another set describing the constraints among these subsystems in the assembled system. This work also includes some discussions on the description of motion (using any possible set of motion variables and admitting any kind of constraint that can be expressed by an invariant), and on the conditions for solving forward and inverse dynamics problems given a mathematical model of a multibody system. Finally, some examples of computational packages based on the novel methodology, along with some case studies, are presented, highlighting the contributions that can be achieved by using the proposed methodology.

Analytical solutions for geometrically nonlinear trusses

This paper presents an analytical method for analyzing trusses with severe geometrically nonlinear behavior. The main objective is to find analytical solutions for trusses with different axial forces in the bars. The methodology is based on truss kinematics, elastic constitutive laws and equilibrium of nodal forces. The proposed formulation can be applied to hyper elastic materials, such as rubber and elastic foams. A Von Mises truss with two bars made by different materials is analyzed to show the accuracy of this methodology.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Distinct conformational properties determined by implicit and explicit representation of protein-solvent interactions. An analytical and computer simulation study

In the protein folding problem, solvent-mediated forces are commonly represented by intra-chain pairwise contact energy. Although this approximation has proven to be useful in several circumstances, it is limited in some other aspects of the problem. Here we show that it is possible to achieve two models to represent the chain-solvent system. one of them with implicit and other with explicit solvent, such that both reproduce the same thermodynamic results. Firstly, lattice models treated by analytical methods, were used to show that the implicit and explicitly representation of solvent effects can be energetically equivalent only if local solvent properties are time and spatially invariant. Following, applying the same reasoning Used for the lattice models, two inter-consistent Monte Carlo off-lattice models for implicit and explicit solvent are constructed, being that now in the latter the solvent properties are allowed to fluctuate. Then, it is shown that the chain configurational evolution as well as the globule equilibrium conformation are significantly distinct for implicit and explicit solvent systems. Actually, strongly contrasting with the implicit solvent version, the explicit solvent model predicts: (i) a malleable globule, in agreement with the estimated large protein-volume fluctuations; (ii) thermal conformational stability, resembling the conformational hear resistance of globular proteins, in which radii of gyration are practically insensitive to thermal effects over a relatively wide range of temperatures; and (iii) smaller radii of gyration at higher temperatures, indicating that the chain conformational entropy in the unfolded state is significantly smaller than that estimated from random coil configurations. Finally, we comment on the meaning of these results with respect to the understanding of the folding process. (C) 2009 Elsevier B.V. All rights reserved.

A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation

A semi-analytical analysis of free vibration of plates with cross-sectional discontinuities due to abrupt changes in thickness is presented. A basic square element divided into suitable subdomains dependent upon the positions of these abrupt changes is used as the basic building element, Admissible functions that satisfy the essential or geometric boundary conditions are used to define the transverse deflection of each subdomain. Continuities in the displacement, slope, moment and higher derivatives between adjacent subdomains are enforced at the interconnecting edges. The resulting global energy functional from the proper assembly of the coupled strain and kinetic energy contributions of each subdomain is then minimized via the Ritz procedure to extract the frequencies and mode shapes. Contour plots of a range of new mode shapes are presented for the enhancement of understanding the dynamic behavior of this class of plates, (C) 2001 Elsevier Science Ltd, All rights reserved.

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem

Analytical Study on the Influence of Geometrical Parameters on the Fatigue Strength of Welds with Undercuts

The purpose of this study is to analyze the influence of geometric parameters on the fatigue strength of the welded joint. The thesis includes the analytical study pertaining to variation of undercut and the weld toe radius. The theoretical part includes the concepts of fracture mechanics, different stages of the crack propagation and finally the results. The numerical results are obtained from FRANC2D/L. The results show that the fatigue strength of the welded structure depends on the parameters of the welds such as the weld toe radius, weld angle, height of the undercut and plate thickness. The results show that the fatigue life can be improved by having the undercut as minimum as possible. However there has been significant variation on the fatigue life of the structure when the weld toe radius is increased.

Analytical and semi-analytical analysis of an artificial satellite's rotational motion

The rotational motion of an artificial satellite is studied by considering torques produced by gravity gradient and direct solar radiation pressure. A satellite of circular cylinder shape is considered here, and Andoyers variables are used to describe the rotational motion. Expressions for direct solar radiation torque are derived. When the earth's shadow is not considered, an analytical solution is obtained using Lagrange's method of variation of parameters. A semi-analytical procedure is proposed to predict the satellite's attitude under the influence of the earth's shadow. The analytical solution shows that angular variables are linear and periodic functions of time while their conjugates suffer only periodic variations. When compared, numerical and analytical solutions have a good agreement during the time range considered.