TM1: Velocity Differential Equation¶
Equation¶
\[
\frac{d\mathbf{v}}{dt} = \frac{\sum\mathbf{F}}{m} - \mathbf{g}
\]
Description¶
This differential equation describes the change in velocity at each time step (\(\Delta t\)) given the forces acting on the object and the gravitational acceleration.
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\(\mathbf{F}\) is the sum of all forces acting on the object.
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\(\mathbf{g}\) is the gravitational acceleration vector, pointing downwards.
- \(m\) is the mass of the object.
Notes¶
To use this differential equation, we need to start from an initial velocity \(\mathbf{v}_0\) and update the velocity at each time step.
Sources¶
Carlucci 20071
Uses¶
Other models/definitions that are used in this model.
Referenced by¶
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Donald E Carlucci. Ballistics: theory and design of guns and ammunition. Crc Press, 2007. ↩