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Dynamical equation for polarization dispersion
Optics Letters, 1991Polarization dispersion in single-mode fiber that contains arbitrary birefringence is described through a vector differential equation. Monte-Carlo simulations using this equation show good agreement with experimental measurements in a randomly birefringent fiber and with a previously reported analytic expression for the length dependence of the ...
Craig D. Poole +2 more
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2003
In this chapter we consider several dynamic equations and present methods on how to solve these equations. Among them are linear equations of higher order, Euler-Cauchy equations of higher order, logistic equations (or Verhulst equations), Bernoulli equations, Riccati equations, and Clairaut equations.
Martin Bohner, Elvan Akin-Bohner
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In this chapter we consider several dynamic equations and present methods on how to solve these equations. Among them are linear equations of higher order, Euler-Cauchy equations of higher order, logistic equations (or Verhulst equations), Bernoulli equations, Riccati equations, and Clairaut equations.
Martin Bohner, Elvan Akin-Bohner
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Hypercomplex equations of dynamics
Soviet Physics Journal, 1991On the basis of the hypercomplex formalism, a system of dynamics equations for material points is introduced, which is a generalization of Newton's equations, and which treats spatial translations and proper rotations in a similar fashion. The notion of generalized forces is formulated in such a way that these have a welldefined physical meaning.
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2004
Since the time when Osborne Reynolds [1] began his life of adventure in investigating the dynamics of turbulence, it has been postulated that the Navier-Stokes and continuity equations hold for the instantaneous values in turbulent flow: $$\frac{{\partial U_i }} {{\partial t}} + U_k \frac{{\partial U_i }} {{\partial x_k }} = - \frac{1} {\varrho ...
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Since the time when Osborne Reynolds [1] began his life of adventure in investigating the dynamics of turbulence, it has been postulated that the Navier-Stokes and continuity equations hold for the instantaneous values in turbulent flow: $$\frac{{\partial U_i }} {{\partial t}} + U_k \frac{{\partial U_i }} {{\partial x_k }} = - \frac{1} {\varrho ...
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Oscillation of third-order nonlinear delay dynamic equation with damping term on time scales
, 2018Ying Sui, Z. Han
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2012
Let us return to Lagrange’s equations of the second kind, which, for the system of N degrees of freedom loaded exclusively with potential forces, take the ...
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Let us return to Lagrange’s equations of the second kind, which, for the system of N degrees of freedom loaded exclusively with potential forces, take the ...
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2001
This chapter proposes a synthetized approach of Lagrange dynamic equations. It deals with the initial formlism based on kinetik and potential energy, and presents the extension to the energy of Hamilton. The prime integrals of motion are presented, with the systematic classification of forces.
Bucur, P. +2 more
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This chapter proposes a synthetized approach of Lagrange dynamic equations. It deals with the initial formlism based on kinetik and potential energy, and presents the extension to the energy of Hamilton. The prime integrals of motion are presented, with the systematic classification of forces.
Bucur, P. +2 more
openaire +1 more source