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Classical Dynamics
A Contemporary Approach
by Jorge V. José and Eugene Saletan
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Chapter Four:
Scattering and Linear Oscillators
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Scattering
- 1. scattering by central forces: general
considerations, the Rutherford cross section
- 2. the inverse scattering problem: general
treatment, example: Coulomb scattering
- 3. chaotic scattering, cantor sets, and
fractal dimension: two disks, three disks, fractal dimension and
Lyapunov exponent
- 4. scattering
of a charge by a magnetic dipole: the Stormer problem, the equatorial
limit, the general case
Linear oscillations
- 1. linear approximation: small vibrations:
linearization, normal modes
- 2. commensurate and incommensurate frequencies:
the invariant torus T, the Poincaré map
- 3. a chain of coupled oscillators: general
solution, the finite chain
- 4. forced and damped oscillators: forced
undamped oscillator, forced damped oscillator
Problems
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