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  • PHYSICS (GENERAL)  (2)
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  • 1976  (2)
  • 1
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    The method of Ritz applied to the equation of Hamilton (1976)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.
    Keywords: PHYSICS (GENERAL)
    Type: Computer Methods in Applied Mechanics and Engineering; 7; Feb. 197
    Format: text
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  • 2
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    Hamilton, Ritz, and elastodynamics (1976)
    In:  Other Sources
    Details
    Publication Date: 2019-06-27
    Description: The theory of Ritz is applied to the equation that Hamilton called the 'Law of Varying Action.' Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin's principles for linear elastodynamics. A brief discussion of Hamilton's law and Hamilton's principle is followed by examples of results for both free-free and cantilever beams with various loadings.
    Keywords: PHYSICS (GENERAL)
    Type: ASME PAPER 76-APM-R , American Society of Mechanical Engineers, 1976
    Format: text
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