Geodesic
Analysis of the Dynamics of Mechanical Systems of Large Dimension with Computer Algebra Systems
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 15-27.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using some developed software package, we analyze the dynamics of a system of 18 linked solids with 32 degrees of freedom in a Newtonian central force field. Using a personal computer for performing symbolic or symbolic-numerical computations, we model the conservative mechanical system (by construction of nonlinear and linearized differential equations of motion) and study both the stability and gyroscopic stabilization of the unperturbed motion.
Keywords: dynamics of systems of solids, computer algebra, software package, stability of motion, degree of instability, gyroscopic stabilization, solution to systems of inequalities. 
@article{SJIM_2009_12_3_a2,
     author = {A. V. Banshchikov},
     title = {Analysis of the {Dynamics} of {Mechanical} {Systems} of {Large} {Dimension} with {Computer} {Algebra} {Systems}},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {15--27},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a2/}
}
TY  - JOUR
AU  - A. V. Banshchikov
TI  - Analysis of the Dynamics of Mechanical Systems of Large Dimension with Computer Algebra Systems
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2009
SP  - 15
EP  - 27
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a2/
LA  - ru
ID  - SJIM_2009_12_3_a2
ER  - 
%0 Journal Article
%A A. V. Banshchikov
%T Analysis of the Dynamics of Mechanical Systems of Large Dimension with Computer Algebra Systems
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2009
%P 15-27
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a2/
%G ru
%F SJIM_2009_12_3_a2
A. V. Banshchikov. Analysis of the Dynamics of Mechanical Systems of Large Dimension with Computer Algebra Systems. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 15-27. http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a2/

[1] Banschikov A. V., Burlakova L. A., Irtegov V. D., Novikov M. A., “Algoritmy kachestvennogo issledovaniya slozhnykh sistem”, Kibernetika i sistemnyi analiz, 1992, no. 1, 129–139

[2] Banschikov A. V., Burlakova L. A., Ivanova G. N., Simonov S. A., “Paket simvolnykh vychislenii “Mekhanik”. Zadachi i struktura”, Pakety prikladnykh programm. Itogi i primenenie, Nauka, Novosibirsk, 1986, 96–105

[3] Banschikov A. V., “Issledovanie ustoichivosti giroramy sredstvami kompyuternoi algebry”, Mat. modelirovanie, 8:4 (1996), 67–78

[4] Banshchikov A. V., Bourlakova L. A., Irtegov V. D., Ivanova G. N., Titorenko T. N., “Symbolic computations in problems of mechanics”, Mathematica J., 8:2 (2001); http://south.rotol.ramk.fi/keranen/IMS99/paper15/ims99paper15.pdf

[5] Banschikov A. V., Burlakova L. A., Irtegov V. D., Titorenko T. N., Programmnyi kompleks LinModel dlya analiza dinamiki mekhanicheskikh sistem bolshoi razmernosti, Svidetelstvo o gos. registratsii programmy dlya EVM No 2008610622, FGU FIPS, 1 fevralya 2008 g.

[6] Simonov S. A., “Algoritm Detsimv vychisleniya opredelitelya v simvolnom vide na EVM”, Pakety prikladnykh programm. Itogi i primenenie, Nauka, Novosibirsk, 1986, 44–53 | MR

[7] Burlakova L. A., Pochtarenko M. V., “Novye vozmozhnosti v pakete simvolnykh vychislenii dlya resheniya zadach mekhaniki”, Pakety prikladnykh programm. Itogi i primenenie, Nauka, Novosibirsk, 1986, 105–112 | MR

[8] Banschikov A. V., Burlakova L. A., “Ob algoritmakh simvolnykh vychislenii pri issledovanii ustoichivosti”, Programmirovanie, 1997, no. 3, 72–80

[9] Chetaev N. G., Ustoichivost dvizheniya, Gostekhizdat, M., 1946

[10] Banschikov A. V., Burlakova L. A., “Informatsionno-issledovatelskaya sistema ‘Ustoichivost’ ”, Izvestiya RAN. Ser. Teoriya i sistemy upravleniya, 1996, no. 2, 13–20

[11] Banshchikov A. V., Bourlakova L. A., “Computer algebra and problems of motion stability”, Mathematics and Computer in Simulation, 57 (2001), 161–174 | DOI | MR | Zbl

[12] Sarychev V. A., “Voprosy orientatsii iskusstvennykh sputnikov”, Itogi nauki i tekhniki. Issledovanie kosmicheskogo prostranstva, 11, VINITI, M., 1978, 5–223

[13] Kozlov V. V., “O stabilizatsii neustoichivykh ravnovesii zaryadov silnymi magnitnymi polyami”, Prikl. matematika i mekhanika, 61:3 (1997), 390–397 | MR | Zbl

[14] Gladun A. V., “Stabilizatsiya orientatsii tverdogo tela s pomoschyu girodinov”, Trudy IPMM NAN Ukrainy, 10, 2005, 32–38 | MR | Zbl