Qualitative dynamics of planar chains

S. Laederich; M. Levi

doi:10.1016/0167-2789(92)90032-I

Qualitative dynamics of planar chains

S. Laederich
, M. Levi

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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,...,n_N) (where N is the number of joints) there exists a periodic motion such that the angle of jth joint changes by 2πn_j 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.

Original language	English (US)
Pages (from-to)	173-182
Number of pages	10
Journal	Physica D: Nonlinear Phenomena
Volume	54
Issue number	3
DOIs	https://doi.org/10.1016/0167-2789(92)90032-I
State	Published - Jan 1 1992

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(92)90032-I

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title = "Qualitative dynamics of planar chains",

abstract = "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.",

author = "S. Laederich and M. Levi",

note = "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.",

year = "1992",

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doi = "10.1016/0167-2789(92)90032-I",

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AU - Laederich, S.

AU - Levi, M.

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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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DO - 10.1016/0167-2789(92)90032-I

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EP - 182

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3

ER -

Qualitative dynamics of planar chains

Abstract

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