The use of Hamilton's principle to derive time-advance algorithms for ordinary differential equations

1996 ◽  
Vol 96 (2-3) ◽  
pp. 129-151 ◽  
Author(s):  
H.Ralph Lewis ◽  
Peter J. Kostelec
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hamilton’S Principle ◽  
Hamilton's Principle

PDE Modeling of a Flexible Two-Link Manipulator

2001 ◽  
Author(s):  
X. Zhang ◽  
S. S. Nair ◽  
V. Chellaboina
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Experimental Studies ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Partial Differential

Abstract The partial differential equations of a flexible two-link manipulator are derived using the Hamilton’s Principle. The model is validated by simulation as well as experimental studies using a two-link setup in the laboratory.

Influence of Cross-Section Distortion on the Bending Vibration of Thin-Walled Beams of H Section

1964 ◽  
Vol 6 (3) ◽  
pp. 211-218 ◽  
Author(s):  
A. D. S. Barr ◽  
T. Duthie
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Reasonable Agreement ◽  
Experimental Results ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Bending Vibration ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Approximate differential equations describing the bending vibration of beams of thin-walled H section, in which the distortion of the cross-section in its own plane is taken into account, are derived from Hamilton's principle using an assumed form for the cross-section deformation. Only the simplest of the cross-sectional deformation configurations which will couple with ordinary bending is considered. The variation with wavelength of the two spectra of frequencies which result from this coupling of the bending and cross-sectional motions is shown for several section geometries. Theoretical curves show reasonable agreement with experimental results from free beams.

scholarly journals Free flexural vibrations of homogeneous beams with symmetrically variable depths

2021 ◽  
Author(s):  
Krzysztof Magnucki ◽  
Ewa Magnucka-Blandzi ◽  
Szymon Milecki ◽  
Damian Goliwąs ◽  
Leszek Wittenbeck
Keyword(s):  
Differential Equations ◽  
Natural Frequency ◽  
Cross Sections ◽  
Equations Of Motion ◽  
Hamilton’S Principle ◽  
Variable Depth ◽  
Hamilton's Principle ◽  
Fundamental Natural Frequency ◽  
The Subject ◽  
Flexural Vibrations

AbstractThe subject of the paper are homogeneous beams of symmetrically variable depth and bisymmetrical cross sections. Free flexural vibrations of these beams are analytically and numerically studied. Based on Hamilton’s principle, the differential equations of motion of these beams are obtained. The equations of motion are analytically solved with consideration of the bending lines of these beams subjected to their own weight. The fundamental natural frequency for exemplary beams is derived and presented in Tables and Figures.

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