Deriving a differential equation for car motion

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SUMMARY

This discussion focuses on deriving a differential equation for a car's motion when it shifts into neutral, emphasizing the importance of air drag as the dominant force affecting motion. The initial velocity is a critical factor, and while gravitational force impacts tire traction, it is not significant if the tires are rotating freely. The conversation highlights the necessity of accurately parameterizing air drag to simplify the modeling process.

PREREQUISITES
  • Understanding of differential equations
  • Knowledge of forces acting on a moving vehicle
  • Familiarity with air drag and its effects on motion
  • Basic principles of friction in mechanical systems
NEXT STEPS
  • Research how to model air drag in differential equations
  • Explore the effects of frictional forces in vehicle dynamics
  • Learn about parameterization techniques for modeling forces
  • Study the role of gravitational force in traction and motion
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Students and professionals in physics, automotive engineering, and applied mathematics who are interested in vehicle dynamics and motion modeling.

cytochrome
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I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation?

I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I don't understand what a downward gravitational force would do for this problem
 
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"Downward gravitational force" (weight) would affect the tire traction. But if you are assuming the tires are rotating freely and not dragging on the ground (no braking or acceleration), that should not be an issue. There will, of course, be friction in the wheel bearings.
 
The dominant force is going to be the air drag. That should make things easy for you, if the air drag can be parameterized accurately.

Chet
 

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