The sliding control law based on vehicle planar equations of motion is used to derive the control laws.
The planar equations of motion for a tapered fly line subjected to tension, bending, aerodynamic drag, and weight are derived.
(8 It is important to note that a system of planar equations (frac{mathrm{d}phi }{mathrm{d}xi }=f_1 phi, z)), (frac{mathrm{d}z}{mathrm{d}xi }=f_2 phi, z)) is called a Hamiltonian system (in classical mechanics) if there exists a function (H phi,z)) such that (f_1=frac{partial H}{partial z}) and (f_2=-frac{partial H}{partial phi }).
This paper expands the historical "Planar model" equation for inertial tree shakers using stacked counter-rotating eccentric-mass energy-wheels and accounts for coupled moments using a "Planar Force and Moment Model".
The present work has developed a simple method for analytically solving most BVPs stated for the planar Poisson equation in a rectangular domain for which, to our knowledge, only series representation of solutions were available.
Most boundary value problems stated for the planar Poisson equation in a rectangle for which series-only representations of solution were known, may thus be solved explicitly in closed-form using the method of images.
The search of analytical closed-form solutions for BVPs for planar Poisson equation - but this is also true for many other problems of mathematical physics - are nowadays little tackled for the benefit of numerical computational methods while the existence of a compact analytical closed-form solution for such problems is always a great advance for a better understanding of underlying physics.
These were then placed into 50 bins along [ − π, π ) and normalised. Also shown in Figure 6(b) are data points obtained from simulations of the full planar Langevin equations.
We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.
Fig. 6 Probability distribution of the phase difference between a pair of E-I oscillators as a function of extrinsic noise strength σ with g, h given by Figure 4. Solid curves are based on analytical calculations, whereas black (gray) filled circles correspond to stochastic simulations of the phase-reduced (planar) Langevin equations.
