A.I. Lurie — works on mechanics
 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
 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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