- #1

IronPlate

- 1

- 0

Let's start with the simple, Newton's Second Law

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Assume mass is constant with time.

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(1) [itex]F=ma[/itex]

(2) [itex]F=m\frac{dv}{dt}[/itex] ; F(t,v)

(3) [itex]F=m\frac{d^{2}u}{dt^{2}}[/itex] ; F(t,u,[itex]\frac{du}{dt}[/itex])

Rate at which v changes with time (acceleration)

(4) [itex]\frac{dv}{dt}=\frac{F}{m}[/itex]

Rate at which F changes with time

(5) [itex]\frac{dF}{dt}=m\frac{d^{3}u}{dt^{3}}[/itex]

Rate at which u changes with time

(6) [itex]\frac{du}{dt}=\frac{1}{m}∫Fdt[/itex]

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Assume m(t), no longer constant.

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Rate at which v changes with time

(7) Same as (4)

Rate at which F changes with time

(8) [itex]\frac{dF}{dt}=m\frac{d^{3}u}{dt^{3}}+\frac{d^{2}u}{dt^{2}}\frac{dm}{dt}[/itex]

Rate at which u changes with time

(9)Absolutely no clue, still working on it.

I'll leave it there.Is there anything wrong with my notation? Does each expression capture the descriptions?