18 research outputs found
Synthesis of Relativistic Wave Equations: The Noninteracting Case
We study internal structure of the Duffin-Kemmer-Petiau equations for spin 0 and spin 1 mesons. We show that in the noninteracting case full covariant solutions of the s=0 and s=1 DKP equations are generalized solutions of the Dirac equation
Asymmetric Duffing oscillator: the birth and build-up of period doubling
In this work, we investigate the period doubling phenomenon in the
periodically forced asymmetric Duffing oscillator. We use the known
steady-state asymptotic solution -- the amplitude-frequency implicit function
-- and known criterion for the existence of period doubling. Working in the
framework of differential properties of implicit functions we derive analytical
formulas for the birth of period-doubled solutions.Comment: 8 pages, 5 figure
Simple model of bouncing ball dynamics. Displacement of the limiter assumed as a cubic function of time
Nonlinear dynamics of a bouncing ball moving vertically in a gravitational
field and colliding with a moving limiter is considered and the Poincare map,
describing evolution from an impact to the next impact, is described.
Displacement of the limiter is assumed as periodic, cubic function of time. Due
to simplicity of this function analytical computations are possible. Several
dynamical modes, such as fixed points, 2 - cycles and chaotic bands are studied
analytically and numerically. It is shown that chaotic bands are created from
fixed points after first period doubling in a corner-type bifurcation. Equation
for the time of the next impact is solved exactly for the case of two
subsequent impacts occurring in the same period of limiter's motion making
analysis of chattering possible.Comment: 8 pages, 1 figure, presented at the DSTA 2011 conference, Lodz,
Polan
Splitting the Dirac equation: the case of longitudinal potentials
Recently, we have demonstrated that some subsolutions of the free
Duffin-Kemmer-Petiau and the Dirac equations obey the same Dirac equation with
some built-in projection operators. In the present paper we study the Dirac
equation in the interacting case. It is demonstrated that the Dirac equation in
longitudinal external fields can be also splitted into two covariant
subequations.Comment: LaTeX, 8 pages, two references adde
Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time
Nonlinear dynamics of a bouncing ball moving in gravitational field and
colliding with a moving limiter is considered. Displacement of the limiter is a
quadratic function of time. Several dynamical modes, such as fixed points, 2 -
cycles and chaotic bands are studied analytically and numerically. It is shown
that chaotic bands appear due to homoclinic structures created from unstable 2
- cycles in a corner-type bifurcation.Comment: 11 pages, 6 figure