Dynamics what moves us 1 Dynamics. General Dynamics Dynamics 2.
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Transcript of Dynamics what moves us 1 Dynamics. General Dynamics Dynamics 2.
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Dynamicswhat moves us
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General Dynamics
• Aristotle
• Newton
• Einstein
where
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Aristotle
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384-322 B.C.Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else that moves it. – Physica, Book VII, Part 1.
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Aristotelian Dynamics
In one dimension:We can make it look like a state equation by using the limit definition of the derivative:
The state equation is deterministic and reversible (but wrong). 4
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Aristotelian Dynamics (cont.)
Solution for , a constant:
Integrating over time gives
where is a constant determined by an initial condition on x(t).
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Aristotelian Dynamics (cont.)
implies
a constant, and as a consequence
Predicts:• No orbits.• No pendulums.
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Isaac Newton
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1642-1727
Philosophiæ Naturalis Principia Mathematica
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Newtonian Dynamics
•Deterministic• Reversible• Right
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Newton’s Laws
I. If , is constant.
II.
III. Every action, , has an equal and opposite reaction,
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Body in a Uniform Gravitational Field
The applied force is
and the initial conditions are
and
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Uniform Gravity (cont.)
From Newton (I) we see right away that
For we have
leading to
For position we find
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An Aside on Units
Fundamental units are
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Unit Measured in…
Length meters
Time seconds
Mass kilograms
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Units of Observed Quantities
Quantity Units Measured in…position metersvelocity meters/secondacceleration meters/second2
force kilogram-meters/second2
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