Equation 6.5 shows that the derivative operation is the Laplace domain, implemented simply by multiplication with the Laplace variable s. This is analogous to this operation in the frequency domain, where differentiation is accomplished by multiplying by jω. So in the absence of initial conditions,...
Deriving Commutation of Variation & Derivative Operators in EL Equation I am trying to do go over the derivations for the principle of least action, and there seems to be an implicit assumption that I can't seem to justify. For the simple case of particles it is the following equality δ(...
QFT - Derivative in Equation of Motion Homework Statement As part of a problem, I need to derive the EOM for a generalized Lagrangian. Before I get there, I'm trying to refresh myself on exactly how these derivatives work because the notation is so bizarre. I am trying to follow a sim...
It is observed that the formulation wherein the axial displacement is neglected and, further, the quadratic term in the strain displacement relation is linearized leads to an equation of motion, which when solved, based on the simple harmonic oscillations assumption, yields exactly the same non-...
Kato, T.: On the Cauchy problem for the (generalized) Korteweg-de Vries equation, in applied mathematics. Adv. Math. Suppl. Stud.8, 93–128 (1983) Google Scholar Kenig, C.E., Ponce, G., Vega, L.: Oscillatory integrals and regularity of dispersive equations. Indiana Univ. Math. J.40...
For any\(\lambda \)they imply the classical Lagrangian equation of motion. Setting\(V=0\), it is $$\begin{aligned}&\left( \frac{\mathrm{d}^2}{\mathrm{d}t^2} + \omega _1^2\right) \left( \frac{\mathrm{d}^2}{\mathrm{d}t^2} + \omega _2^2\right) q\nonumber \\&\qua...
Moreover, the present model can be viewed as a forced harmonic-oscillator of the first-order in a fractional form, and it may be of practical interest in engineering science. Although Equation (1) seems simple, obtaining its exact solution is not an easy task due to several factors that ...
We incorporate the time-derivatives of the potential function to account for the velocities of intermediate target points, thereby resolving the conflict between the fixed-point chasing logic of the DRL motion controller and the potentially erratic movements of the intermediate target points. To enhance...
Moreover, the present model can be viewed as a forced harmonic-oscillator of the first-order in a fractional form, and it may be of practical interest in engineering science. Although Equation (1) seems simple, obtaining its exact solution is not an easy task due to several factors that ...
Moreover, the present model can be viewed as a forced harmonic-oscillator of the first-order in a fractional form, and it may be of practical interest in engineering science. Although Equation (1) seems simple, obtaining its exact solution is not an easy task due to several factors that ...