Abstract

En We consider the effect of a linear constraint on the small oscillations about an equilibrium position of a conservative dynamical system which has just three degrees of freedom. Explicit expressions are presented for the eigenfrequencies and eigenvectors of the constrained system in terms of the eigenfrequencies and eigenvectors of the unconstrained system. The unconstrained system is described in terms of two positive definite 3×3 matrices with which two concentric ellipsoids may be associated. A ‘plane’ corresponds to the linear constraint. It is seen that in general it is possible to choose two constraints such that the constrained motion has a double eigenfrequency,or equivalently, two central planes may be chosen which cut the two concentric ellipsoids in a pair of similar and similarly situated ellipses.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.