Classical Mechanics 2

47 views3 pages
Published on 25 Jun 2011
School
UTSG
Department
Physics
Course
PHY100H1
Classical Mechanics 2!
What is Chaos?
Chaos is a state of a system in which the initial conditions strongly
influence the routes followed by other objects in the system. There is a
"strong sensitivity to the initial conditions".
Thought Experiment:
The successful application of Newtons Laws in determining the motion of the planets
in the Solar System led Pierre Simon de Laplace (1749-1827) to conclude that the
universe behaves in a deterministic manner.
If we knew the masses of, forces on, and initial positions and velocities of every
object, then we could predict their future trajectories or paths exactly. Although this is
true in many situations, it is not always possible.
Henri Poincare (1854-1912) calculated the evolution of three bodies interacting via
Newton's Law of Gravitation and found that some configurations were highly
unstable.
It was possible under certain conditions for one of the objects to be ejected from the
system. Poincare discovered an example of what is now called chaos.
What is Work?
Energy is the ability to do work. If something has energy, then it can apply
a force to an object and cause the object to move.
Work is done when a force that is applied to an object moves that object.
Work = Force x Distance
Suppose a force F acts on an object. If the object moves a distance d due to
the applied force, then the work done on the object is the product of F and
d.
Kinetic Energy
Kinetic energy is associated with an objects motion.
Potential Energy
Potential energy is associated with the position of an object near
something that can exert a force, such as a planet. A ball placed on a ledge
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Document Summary

Chaos is a state of a system in which the initial conditions strongly influence the routes followed by other objects in the system. The successful application of newton"s laws in determining the motion of the planets in the solar system led pierre simon de laplace (1749-1827) to conclude that the universe behaves in a deterministic manner. If we knew the masses of, forces on, and initial positions and velocities of every object, then we could predict their future trajectories or paths exactly. Although this is true in many situations, it is not always possible. Henri poincare (1854-1912) calculated the evolution of three bodies interacting via. Newton"s law of gravitation and found that some configurations were highly unstable. It was possible under certain conditions for one of the objects to be ejected from the system. Poincare discovered an example of what is now called chaos.

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