CAUSAL CLASSICAL THEORY OF RADIATION DAMPING

Classical Damping, Non-Classical Damping and Complex Modes

with initial conditions r(0) = do and ṙ(0) = vo. If the system is un-damped (C = 0N×N), the free response of the system will not decay with time, and a suitable trial solution to the differential equation (1) is r(t) = r̄ sin(ωnt), where r̄ is a constant vector of dimension N . Differentiating r(t) twice, r̈(t) = −ω2 nr̄ sin(ωnt), and substituting the trial solution into equation (1) we obtain − ω2...

Rayleigh’s Classical Damping Revisited

Proportional damping is a widely used approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than ten decades. A major limitation of the mass and stiffness proportional damping approximation is the lack of generality of the model to allow for experimentally observed variation of damping factors with respect to vibration f...

Radiation Damping

The basic formulae for the damping of the energy and betatron oscillations are derived. The results are applied to a number of examples of different lattice designs in which radiation damping effects are important. Methods of modifying and measuring the damping rates are also discussed.

Resonant States and Classical Damping

Using Koopman’s approach to classical dynamical systems we show that the classical damping may be interpreted as appearance of resonant states of the corresponding Koopman’s operator. It turns out that simple classical damped systems give rise to discrete complex spectra. Therefore, the corresponding generalized eigenvectors may be interpreted as classical resonant states.

Physics: B. Podolsky on King's Classical Theory of Radiation