"The History of Computer Algebra Application in Mechanics
in Russia (Soviet Union)"
G.B.Efimov, M.V.Grosheva
Keldysh Institute of Applied Mathematics RAS
Institute of Mechanics Moscow State Lomonosov University
Moskow, 125047, Miusskaya sq.4, Russia
efimov@applmat.msk.su grosheva@inmech.msu.su
Present Review considers the History of Mechanical
Applications of Symbolical Algebraic Manipulations (SAM) or
Computer Algebra (CA) in our country - for almost forty years.
>From the very beginning mechanicians was among the leaders of
SAM application - due to vast problems, important for them
(spacecraft dynamics, theory of strength), as well as due to
presence and readiness of experts, capable to develop
mathematical methods and to apply/develop computer programs for
SAM.
The first attempts of computer symbolical manipulations
in Soviet Unions were made more than thirty years ago. In the
work of Nobel laureate L.V.KANTORORVICH and his followers the
problems of SAM and their applications were considered, in
particular in the theory of elasticity. N.N.YANENKO and his
colleagues solved the problems of differential schemes
theory. D.E.OKHOTSIMSKY, V.A.BRUMBERG and others applied SAM
in celestial mechanics. M.CHUBAROV investigated a stability
problem in linear systems. Despite the computers had only the
few K of memory at that time, some interesting problems were
solved successively with them.
In the middle of 1960's and in the beginning of 1970's the
old groups of workers were expanded and new ones have arisen in
the area of SAM. The groups were working in Moscow, Leningrad,
Novosibirsk, Gorky, Tomsk, Kazan, Harkov, Irkutsk, Vilnius.The
areas of researches were: stability in mechanics, oscillation and
control theory, celestial mechanics and elasticity, group theory
in fluid mechanics, mathematics, physics and computorial
problems. In Kiev V.A.GLUSHKOV with his colleagues have created
the computer "MIR-2", the first realization of the symbolic-
numerical language ANALYTIK by hardware means. Many mathematical
and mechanical problems were solved and many non-trivial
algorithms realized on these computers. Later ANALYTIK was
realized both by hardware on Hulliet-Packers and IBM machines
and by software. SAM systems were created with both high and low
level languages. As an interesting example of high level
language we can mention V.F.TURCHIN with his original language
Refal. S.S.LAVROV and his colleagues worked on Lisp.
A.P.ERSHOV was initiator of creation the universal tipe SAM. From
the other hand, applied specialists, physicists and mechanicians,
often created specialized SAM program systems for solving
their problems, and sometimes preferred Algol or Fortran.
Numerous applications had very large range: from nuclear physics
and General Relativity, multi-bodies dynamics and stability to
differential geometry and analysis.
In the end of the 70-ies SAM were used more often and have
obtained rather wide popularity. Conferences in Novosibirsk,
Irkutsk, in Moscow University contributed to this popularity. At
the known conferences in Dubna the foreign systems (REDUCE,
for example) were demonstrated and widely distributed. REDUCE
algorithms were created in mechanics applications domain as well
as in physics one.
The large event was the great conference on SAM in mechanics
in 1984 in Gorky. The majority of experts in SAM from our
country were participating it, and achievements of works for
20 years were demonstrated. There were such known scientists
among participants as A.A.SAMARSKY, N.N.GOVORUN, D.M.KLIMOV,
V.M.MATROSOV, D.V.SHIRKOV and others. The programmers have
demonstrated the SAM systems, physicists, mechanicians and
mathematicians presented various problems and algorithms.
In theory of elasticity, mechanics of fluid and celestial
mechanics SAM were used for construction of solutions in
series. Formal derivation of equations of movement, their
averaging, analysis of stability, generation of numerical
programs for simulation - were applied for various difficult
mechanical systems. The large difference schemes, formulas of
estimation of accuracy were formed. The group properties
of systems of equations, their integrals were investigated.
The SAM applications in multi bodies dynamics (more then
15 groups from Moscow, S-Petersburg, Irkutsk, Perm, Vilnius etc.)
were analyzed in special conferences and work-shops in
S-Petersburg, Vilnius, Irkutsk and Moscow University.
At present SAM became recognized and customary tool for solution
of problems of mechanics of multi-body systems, celestial
mechanics, cavitation, strength, physics, theory of control.
Now many domestic systems, including specialized, have finished
the work. Their role was taken by the programs in systems
REDUCE, MAPLE, MATHEMATYCA and other ones. But the experts on
SAM and their applications in various areas continue to
work. The experience of work, solution of specific SAM problems
is present. SAM are applied in new areas (chemistry, verification
of programs etc.), but SAM conventional applications in
mechanics as always are popular.
SAM are widely used in mathematical education from the very
beginning: in formation system programmers on SAM, for
training for SAM-systems, for mechanics and physics education. In
many Universities the courses on SAM, their systems, algorithms
and applications are read. The students are taught to work with
SAM, to construct and realize symbolical algorithms, to apply
SAM in mechanics, mathematics, physics, to participate in
development of systems. The geography of SAM application in
education has very large domain: from S.Petersburg to Irkutsk,
>from Perm and Dubna to Kiev and Lvov.
Information about many systems and mathematical and
mechanical algorithms in them were assembled by authors of this
report. The modern data are collecting in information bank on SAM:
"Computer Symbolic manipulations in problems of mechanics"
(Institute of Mechanics. Moscow State Lomonosov University.
Michurynski pr.1, Moscow 117192, Russia. M.V.Grosheva: tel.(095)
939-5478,e-mail: grosheva@inmech.msu.su).
The work was carried out under support of RFFI grant N 96-15
-97229, N 98-01-00941 and Russian Universities, Mathematical
Simulation.
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transformations. Moscow, Nauka, 1988, 5-30. (In Russian).
[2] Grosheva M.V., Samsonov V.A. Information bank: Computer
Symbolic manipulations in problems of mechanics. - In:
Computer Analytical manipulations in automatic of scientific
research. Vilnius, 1990, p.92. (In Russian).
[3] Efimov G.B., Grosheva M.V. On History of use the Computerized
Symbolical Manipulation's in Mechanics. - Preprint of Inst.of
Mech. Moscow St. Lomonosov University, No 16, Moscow. 1995.
44 pp. (In Russian).
[5] Miola A.M., Pottosin I.V. A bibliography of soviet works in
algebraic manipulations. - SIGSAM Bull., 1981, 15, N 1, 5-7.
[6] Brumberg V.A., Tarasevich S.V., Vasiliev N.N. Specialized
celestial mechanics systems for symbolic manipulations.-
Celest. Mech. 1989, 45, 149-162.