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Pavel Zhilin
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A.I. Lurie — works on mechanics

Lurie2 (9K) A man cannot choose his birthday or birth place. However, time and habitation country significantly influence upon the making of a person and determine the character of his activity. Nevertheless, at all times and in all countries the individuals are born, who are realized as self-independent and self-sufficient creatures... next

The rod theory and modern mechanics

The theory of thin rods has played outstanding role in the history of development of mechanics and mathematical physics. In order to show the contribution of the theory of thin rods to the development of natural sciences more clearly, let us point out only some facts... next

On direct approaches to construction of the shell theory

As a general rule, when speaking of the foundations of shell theory we think of the following problems: a rational derivation of the basic equations of two-dimensional shell theory from the equations of three-dimensional theory of elasticity; a formulation of the boundary conditions; an estimate of the accuracy of the equations so derived... next

Symmetries and orthogonal invariants

Symmetries and orthogonal invariants are important theoretical tools for many fields of mechanics. Therefore these tools must be applicable to all objects widely used in mechanics. Unfortunately this is not so. The application of the classical theory of symmetry leads to the meaningless results in shell theory and not only in shell theory... next

Rigid body oscillator

The nonlinear (linear) oscillator is the most important model of classical physics. An investigation of many physical phenomena and a development of many methods of nonlinear mechanics had arisen due to this model. At the same time, the necessity of construction of models with new properties was recognized... next

Euler angles and the problem of free rotations of rigid bodies

Ejler3 (18K) Free rotation of rigid bodies was the first problem that was completely solved in dynamics of rigid bodies. Originally it was studied by Leonard Euler. Later Poinsot offered the famous geometrical interpretation to show real rotation of the body. In modern literature this problem is called the case of the integrability by Euler Poinsot. Up to now no theoretical adaptations were made to the classical solution, the description of which is presented in all books on dynamics of rigid bodies. The classical solution allows perfectly to find the rotations, i.e. angular velocities, of the body. However, the determination of the turns, i.e. angles, does not impress so much... next

Dry friction and Painleve paradoxes

The friction is one of the most widespread phenomena in a Nature. The manifestations of friction are rather diverse. The laws, with which the friction in concrete situations is described, are diverse as well. Most popular in the applications are two laws of friction: the linear law of viscous friction and so-called dry friction. The viscous friction is well investigated, and its manifestations are clear and are easily predicted. It cannot be said about the laws of dry friction, though they are studied and are used in practice already more than two hundred years... next

Inelasticity: the important experimental facts

A behavior of solid structures under an external loading has been studied during several centuries. However intensive and task-oriented investigations had begun in XIX century and are carried out till the present time. All known materials can be separated on two different classes: elastic materials and all others. In general, the fundamentals of the nonlinear theory of elasticity may be considered as completely developed. For inelastic materials the situation is quite different... next

Piezoelectric materials

The brothers Pierre and Jacques Curie, in 1880, were the first to experimentally demonstrate piezoelectric behavior in a series of crystals, including quartz and Rochelle salt. The first attempt to derive the theory of piezoelectricity was made by Voigt in 1910... next

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