Tangent circles, differential
- Author:
- Ryan Hirst
Proposition: Make a circle seek tangency with a given circle.
Vector formula for circle through three points: http://www.geogebratube.org/material/show/id/34739
Notes:
Here, force is proportional to distance from the nearest point of tangency. (k)
Damping force proportional to velocity. (λ)
Convergence time is just for fun. Lower λ to bounce around the solution. Increase λ to go straight to it.
Update script in the variable t:
SetValue[accel1, (-k DC cosβ - λ v )/m1]
SetValue[Δv, accel1 Δt]
SetValue[v, v + Δv]
SetValue[Δx, v Δt]
SetValue[τ, Angle[τ - Δx/a]]
The choice of a parametric circle for A is a bit tricky in Geogebra.
Clearly, the solution is more direct. Let D approach the line AO.
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Tangency Problem of Appolonius
- Geometric Solution: http://www.geogebratube.org/material/show/id/34645
- Differential Solution: →a.Seek model (one circle) b. Solution, v.1: http://www.geogebratube.org/material/show/id/34855 c. Solution v.2, improved: http://www.geogebratube.org/material/show/id/35386