By Shayne Lindsey; Victor Quinn
This publication offers an exhaustive method of Classical and Continuum Mechanics.
summary: This booklet presents an exhaustive method of Classical and Continuum Mechanics
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Simplified overview of uses The value of the Hamiltonian is the total energy of the system being described. For a closed system, it is the sum of the kinetic and potential energy in the system. There is a set of differential equations known as the Hamilton equations which give the time evolution of the system. Hamiltonians can be used to describe such simple systems as a bouncing ball, a pendulum or an oscillating spring in which energy changes from kinetic to potential and back again over time.
Gravitational potential energy Gravitational energy is the potential energy associated with gravitational force. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. The gravitational force keeps the planets in orbit around the Sun A trebuchet uses the gravitational potential energy of the counterweight to throw projectiles over long distances For example, consider a book, placed on top of a table.
If the work done moving along a path which starts and ends in the same location is zero, then the force is said to be conservative and it is possible to define a numerical value of potential associated with every point in space. A force field can be re-obtained by taking the negative of the vector gradient of the potential field. For example, gravity is a conservative force. The associated potential is the gravitational potential, often denoted by φ or V, corresponding to the energy per unit mass as a function of position.