Geodesic
State equilibrium stability of conservative systems in one particular case
Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 37 
Ranislav Bulatović. State equilibrium stability of conservative systems in one particular case. Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 37 . http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a2/
@article{TAM_1994_20_1_a2,
     author = {Ranislav Bulatovi\'c},
     title = {State equilibrium stability of conservative systems in one particular case},
     journal = {Theoretical and applied mechanics},
     pages = {37 },
     year = {1994},
     volume = {20},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a2/}
}
TY  - JOUR
AU  - Ranislav Bulatović
TI  - State equilibrium stability of conservative systems in one particular case
JO  - Theoretical and applied mechanics
PY  - 1994
SP  - 37 
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a2/
LA  - en
ID  - TAM_1994_20_1_a2
ER  - 
%0 Journal Article
%A Ranislav Bulatović
%T State equilibrium stability of conservative systems in one particular case
%J Theoretical and applied mechanics
%D 1994
%P 37 
%V 20
%N 1
%U http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a2/
%G en
%F TAM_1994_20_1_a2

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Conservative holonomic system, whose potential energy $P\in C^s$, $s\geq2$, in normal coordinates is: $P(\mathbf q)=\frac12\langle C(\mathbf q)\mathbf x,\mathbf x\rangle+P_k(\mathbf q)+W(\mathbf q)$, where $\mathbf q=(\mathbf x,\mathbf y)$, $\mathbf x\in\mathbb R^m$, $\mathbf y\in\mathbb R^n$, $C(\mathbf 0)=\operatorname{diag}(\omega^2_1,\dots,\omega^2_m)$, $P_k(\mathbf q)$ homogeneous polynomial of degre $k$, $k$ and $W(\mathbf q)=O(|\mathbf q|^{k+1})$ is studied. In a case when function $P_k(\mathbf 0,\mathbf y)$ has not minimum (has strict minimum) in $\mathbf y=\mathbf 0$, stability (instability) of the state of equilibrium $\mathbf q=\dot{\mathbf q}=\mathbf 0$ is proved. This statement, in a case when $P_k(\mathbf 0,\mathbf y)\geq0$, is completed with one additional instability criterion.