"OPUS"  analitical calculation systems
use for nonlinear particle dynamic analysis.
"OPUS" has been written by means
of ACS (analitical calculation systems) and based on the generalization
of the corresponding methods to find and research the periodic solution
stability of the usual differential equations using the critical points
of the Saction function [1, 2, 3]. "OPUS" [2,
3] is based on two statements of Poincare:
  the first is
"... periodic solutions are the only way we could try to enter
the field concidered to be inaccessible",
 the second "...a periodical solutions
can disappear in case of mergence with the other one ", e.i.
" the periodic solutions disapear in pairs similarly the real
roots of the algebraic equations" ([1], p.75).
For n  approximation (n=1,2,...)
in analitical form "OPUS" allows:
 calculating the stable
weighing zones of different bodies and particles (from elementary
to macro) without external feedback in and out of the resonance range,
 finding the periodic solutions of the differential
equations, not containing an explicit small parameter, for lagrange's
and unlagrange's systems, where dissipation and disturbance are taken
into consideration,
 analyzing the nonlinear systems stability
near the periodical solutions,
 optimizing the system dynamics using parameters,
 determining the spectrum and conditions
of chaos beginning for nonlinear systems.
In the lagrange system case:
L = T{dX(1)/dt,...,dX(n)/dt}  U{X(1),...,X(n),t},
H = T + U,
T=SUM(I1=1...n)[dX(I1)/dt]**2,
Let U{X,f(t)}=U{X,f(t+T)} and F =
F {dX(I1)/dt}  a dissipative function,
"OPUS" is based on going to the new Y(I1,I2,I3)
variables from the previous X(I1), from H{X(I1),dX(I1)/dt,t}
Hamiltonian with I1:=1,2,...n, where n  freedom degree number,
X(I1), dX(I1)/dt  phase variables coordinates, velosity
to the new "hamiltonian" S(Y(I1,I2,I3)) with the new
dissipative function R{Y(I1,I2,2)} and "freedom degrees"
number  n*(k + 1), where Y(I1,I2,I3)  the new phase variables
I1=1,2,...n, I2:=0,1,...,k, where k  the corresponding approximation
(quantity of harmonics taken into account), I3:=1,2, Y(I1,I2,I3=1)
 coordinates, Y(I1,I2,I3=2)  velosity,
let f(t) = SUM(I2=0...w){Y(0,I2,1)*cos(I2*t)
+ [Y(0,I2,2)/I2]*sin(I2*t)}, X(I1)=SUM(I2=0...k){Y(I1,I2,1)*cos(I2*t)
+ [Y(I1,I2,2)/I2]*sin(I2*t)},
Y(I1,I2,I3)  slowly changing amplitudes, dY(I1,0,1)/dt = Y(I1,0,2).
So in the systems without dissipation the problem lies in finding of
Sfunction extremums relatively to Y(I1,I2,I3) and the task parameters:
D1(J1) = dS/dY{J1}, D2(J1,J2) = dD(J1)/dY(J2) = d2S/dY{J1}*dY{J2}, J=f(I1,I2,I3).
The S  function method is published in the journals and tested in the
problems, some of them are represented as the examples in the paper
a),b).
The examples of "OPUS" use
for IBM PC/AT is represented below:
a)  for instable stationary
state dynamic stability researching of the autonomoies system,
b)  for the pendulum
of P.L. Kapitsa with the vibrating suspention point in and out of resonanse
zone and for dynamics of particles considered their characteristics
(charges and moments) in field's.
"OPUS" is also a method to calculation
the stable confinement and levitation control of the bodies and particles
movement. So the new "OPUS" technologies and available application
fields are suggested to you [3]:
1. Development of the resonant traps for particles of different
types and sizes (from elementary particles to macroparticles) using
no feedback; studies of properties of individual particles and their
dynamics in such traps (e.g. atoms and molecules) and packing them
on the surfaces of solids  molecular technology); development of
the resonant traps for plasma; obtaining the selfconfined plasma.
2. Development of new contactless methods of treatment, preventive
treatment and diagnostics, based on the resonant effects of electromagnetic
fields on the biological systems; to regulate of biochemical reactions
inside the biological organisms.
3. Separation of different kinds of powders (ferromagnetic, abrasive
etc.), which are used, for example, in the production of the magnetic
recording medium materials (for magnetic disks or tapes).
4. Development of new resonant supersensitive transducers of the
fields (electromagnetic, acoustic, hydrodynamic, seismic, gravitational).
5. Robotization  electromagnetic suspention of the details, their
contactless orientation in space and control during the assembling
of different mechanisms and devices.
6. Suspension in the air and transference of the different bodies
in the necessary direction (rotors of engines, toys, magnetically
levitated trains).
SRC "IKAR" would be glad
to cooperate with the researchers, who are interested in this
technologies, in particular in technologies:
 development of resonant traps where plasma is to be used;
 selfconfinement
plasma  ball lightning;
 development of the
new noncontact methods for prophylactics, treatment and diagnostics
on the basis of effect of resonant fields on biological systems;
biochemical and chemical reaction's control.
We already have received
interesting outcomes in these directions.
Literature:
 Poincare A. New methods of celestial mechanics.M.: 1971,
v.1.
 Shironosov V.G. About stability of unstable states, bifurcation
and chaos of nonlinear dynamic systems (Ob ustoichivosti neustoichivykh
sostoyanii, bifurkatsii, khaose nelineinykh dinamicheskikh system)
(in Russian).  DAN SSSR, 1990, v. 314, No. 2, p. 316320.
 Shironosov V.G. Resonance in physics,
chemistry and biology. Izhevsk. Publ. House "Udmurtia University",
2001. 92 p.
