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Research Papers

The Inverse Problem of Linear Lagrangian Dynamics

[+] Author and Article Information
Rubens Goncalves Salsa, Jr

Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: rsalsa@berkeley.edu

Daniel T. Kawano

Department of Mechanical Engineering,
Rose-Hulman Institute of Technology,
Terre Haute, IN 47803
e-mail: kawano@rose-hulman.edu

Fai Ma

Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: fma@berkeley.edu

George Leitmann

Department of Mechanical Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: gleit@berkeley.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 28, 2017; final manuscript received December 11, 2017; published online January 4, 2018. Assoc. Editor: Walter Lacarbonara.

J. Appl. Mech 85(3), 031002 (Jan 04, 2018) (10 pages) Paper No: JAM-17-1539; doi: 10.1115/1.4038749 History: Received September 28, 2017; Revised December 11, 2017

A comprehensive study is reported herein for the evaluation of Lagrangian functions for linear systems possessing symmetric or nonsymmetric coefficient matrices. Contrary to popular beliefs, it is shown that many coupled linear systems do not admit Lagrangian functions. In addition, Lagrangian functions generally cannot be determined by system decoupling unless further restriction such as classical damping is assumed. However, a scalar function that plays the role of a Lagrangian function can be determined for any linear system by decoupling. This generalized Lagrangian function produces the equations of motion and it contains information on system properties, yet it satisfies a modified version of the Euler–Lagrange equations. Subject to this interpretation, a solution to the inverse problem of linear Lagrangian dynamics is provided.

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