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- 7.1 Tautochrone problem
- 7.1.1 Non-relativistic case
- 7.1.2 Relativistic case
- 7.2 Inverse problems
- 7.2.1 Finding potential from a period-energy dependence
- 7.2.2 Finding potential from scattering data
- 7.2.3 Stellar systems
- 7.3 Motion through a viscous fluid
- 7.3.1 Entrainment of fluid by a moving wall
- 7.3.2 Newton's equation with fractional term
- 7.3.3 Solution by the Laplace transform method
- 7.3.4 Solution by the Green functions method
- 7.3.5 Fractionalized fall process
- 7.4 Fractional oscillations
- 7.4.1 Fractionalized harmonic oscillator
- 7.4.2 Linear chain of fractional oscillators
- 7.4.3 Fractionalized waves
- 7.4.4 Fractionalized Frenkel-Kontorova model
- 7.4.5 Oscillations of bodies in a viscous fluid
- 7.5 Dynamical control problems
- 7.5.1 PID controller and its fractional generalization
- 7.5.2 Fractional transfer functions
- 7.5.3 Fractional optimal control problem
- 7.6 Analytical fractional dynamics
- 7.6.1 Euler-Lagrange equation
- 7.6.2 Discrete system Hamiltonian
- 7.6.3 Potentials of non-concervative forces
- 7.6.4 Hamilton-Jacobi mechanics
- 7.6.5 Hamiltonian formalism for field theory
- References
