Tangent circles, differential
- 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. ____________ 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