TY - JOUR
T1 - Qualitative dynamics of planar chains
AU - Laederich, S.
AU - Levi, M.
N1 - Funding Information:
2Supported in part by AFOSR grant 0.144-85. Permanent address: Department of Mathematics, Boston University, 111 Cummington Street, Boston, MA 02215, USA.
PY - 1992/1/1
Y1 - 1992/1/1
N2 - In this paper we derive the equations of motion and analyze some aspects of the dynamics of planar chains. We show that (a) for any integer vector n=(n1,...,nN) (where N is the number of joints) there exists a periodic motion such that the angle of jth joint changes by 2πnj during one period; (b) the straight configuration is (nonlinearly) stable and that any "folded" rectilinear configuration is unstable; (c) the Coriolis effects play no role in stability of these rectilinear configurations, in contrast to other problems such as the stabilizing effect on the spinning top.
AB - In this paper we derive the equations of motion and analyze some aspects of the dynamics of planar chains. We show that (a) for any integer vector n=(n1,...,nN) (where N is the number of joints) there exists a periodic motion such that the angle of jth joint changes by 2πnj during one period; (b) the straight configuration is (nonlinearly) stable and that any "folded" rectilinear configuration is unstable; (c) the Coriolis effects play no role in stability of these rectilinear configurations, in contrast to other problems such as the stabilizing effect on the spinning top.
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U2 - 10.1016/0167-2789(92)90032-I
DO - 10.1016/0167-2789(92)90032-I
M3 - Article
AN - SCOPUS:44049125090
SN - 0167-2789
VL - 54
SP - 173
EP - 182
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3
ER -