Edward Carey Francis

Pars, L. A.

doi:10.1112/jlms/s1-43.1.368

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, we will not be very surprised if we find the same mistake again in the new Iiterature (as several times in the past). This fact, which has been overseen by many authors during the last 100 years and as many times corrected afterwards, is explained for example in PARS (31], NEIMARK&FUFAEV (28] and in WHITTAKER [44]. These authors show that the equations of motion of a dynamical system with non-holonomic constraints cannot be obtained via calculus of variations by applying the multiplier rule in the usual way.…”

Section: Nonholonomic Systems: An Elementary But Common Mistakementioning

confidence: 89%

“…This caused the search for more general variational principles as well as for new formalisms for obtaining the correct equations of motion for non-holonomic systems. Since this fact falls into oblivion with regularity, it might be useful to illustrate it with an example borrowed from PARS [31] (see pages 529 and 530). Consider a particle P with position characterized by the cartesian Coordinates (x, y, z) in inertial space and subjected to the single non-holonomic constraint …”

Section: Nonholonomic Systems: An Elementary But Common Mistakementioning

confidence: 98%

See 1 more Smart Citation

Modern Analytical Methods Applied to Mechanical Engineering Systems

Hagedorn

Seemann

1998

Modern Methods of Analytical Mechanics and Their Applications

View full text Add to dashboard Cite

In the following lectures modern analytical methods are applied to several industrial systems. The first application is the use of singular perturbation analysis in the eigenvalue problern of a vibrating string with a small bending stiffness. This models the behavior of overhead transmission lines. A more complicated system is the eigenvalue problern of a cylinder vibrating in an cylindrical duct, which is filled with a viscous fluid.The next lecture shows the use of analytical methods in the modeHing of ultrasonic motors. Of special interest is the coupling between the electric and the mechanical field in the piezoelectric patches. Here HAMILTON's principle for electromechanical systems is of gre(!.t importance. It allows to find approximate solutions fulfilling additional constraint equations.In overhead transmission lines also wind excited vibrations are important as they may lead to fatigue. Models for the corresponding mechanism are given as well as the analysis of special vibration absorbers designed by modern methods of vibration theory.The last lecture deals with three problems of nonholonomic systems and of stability and instability theorems. The first problern shows that the augmented Lagrangian is not stationary for nonholonomic systems. The second gives a simple exercise in LIAPUNOV stability. The last deals with the LAGRANGE-DIRICHLET theorem and its inverses.

show abstract

Section: Nonholonomic Systems: An Elementary But Common Mistakementioning

confidence: 89%

Section: Nonholonomic Systems: An Elementary But Common Mistakementioning

confidence: 98%