Hamiltonian Mechanics

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6 Conclusion

Many topics remained outside from these lecture notes, differently from the original planning. These include a treatment of Poisson and Jacobi manifolds, a detailed analysis of phase-space reduction, a discussion of geodesic motions on sub-riemannian geometry, the introduction of contact geometry – the odd sister of symplectic geometry – and its use for thermodynamics and dissipative systems, Lax pairs and the modern theory of integrable systems, monodromy, rigid bodies from the lagrangian and hamiltonian point of view and, last but not least, semiclassical analysis and quantization.

The topic is vast, interesting and very actively developed. I hope the selection made for this course has challenged you, that it will help you in the rest of your career and that it did show in a new light some of the remarkable and beautiful aspects of classical mechanics.

Bibliography

Index

A

acceleration, section 1.1

action, section 1.2

action

critical point, section 1.2

B

Banach space, section 1.2

C

configuration, section 1.1.1

space, section 1.1.1

D

degrees of freedom, section 1.1.1

diffemorphic, example 1.3

E

elliptic integrals, example 1.1

equations of motion, section 1.1.1

Euler-Lagrange equations, theorem 1.1

F

frames of reference, section 1.1

Frechet

derivative, section 1.2

differentiable, section 1.2

G

generalized

coordinates, section 1.1.1

velocities, section 1.1.1

gravitational constant, example 1.2

H

Hamilton’s principle, section 1.2

I

inertia, section 1.1

L

lagrangian, section 1.2

N

Newton

principle of determinacy, section 1.1.1

second law, section 1.1

universal gravitation, example 1.2

P

pendulum, example 1.1

ideal, example 1.1

point particle, section 1.1

system, section 1.1.1

position, section 1.1

principle of least action, section 1.2

S

spring, example 1.1

constant, example 1.1

Hooke’s law, example 1.1

state space, section 1.1.1

V

variation, item 5

velocity, section 1.1