单位切向量、法向量与副法向量（Frenet标架）动态演示

GeoGebra 命令及参数

1. CurveCartesian((f(t), g(t), h(t)), t, -10, 10) → r_{0}
2. Vector(P, P + (f'(t), g'(t), h'(t))) → r'
3. Vector(P, P + UnitVector[r']) → T
4. Vector(P, P + (F'(t), G'(t), H'(t))) → T'
5. Vector(P, P + UnitVector[T']) → N
6. Vector(P, P + T ⊗ N) → B
7. CurveCartesian(f((-t)), g((-t)), h((-t)), t, -10, 10) → r_{1}
8. CurveCartesian(f((3 * t)), g((3 * t)), h((3 * t)), t, -10, 10) → r_{2}
9. Integral(sqrt(f'(t)^(2) + g'(t)^(2) + h'(t)^(2)), 0, t) → s
10. Vector(Q, Q + (f_{1}'(t), g_{1}'(t), h_{1}'(t))) → v_{1}
11. Vector(Q, Q + (f_{1}''(t), g_{1}''(t), h_{1}''(t))) → a_{1}
12. Vector(R, R + (f_{2}'(t), g_{2}'(t), h_{2}'(t))) → v_{2}
13. Vector(S, S + (f_{3}'(s), g_{3}'(s), h_{3}'(s))) → v_{3}
14. Vector(S, S + (f_{3}''(s), g_{3}''(s), h_{3}''(s))) → a_{2}
15. Vector(S, S + (f_{3}''(s), g_{3}''(s), h_{3}''(s))) → a_{3}
16. Vector(Q, Q + UnitVector[v_{1}]) → T_{1}
17. Vector(R, R + UnitVector[v_{2}]) → T_{2}
18. Vector(S, S + UnitVector[v_{3}]) → T_{3}
19. Vector(Q, Q + (F'((-t)), G'((-t)), H'((-t)))) → T_{1}'
20. Vector(R, R + (F'((3 * t)), G'((3 * t)), H'((3 * t)))) → T_{2}'
21. Vector(S, S + (F'(s), G'(s), H'(s))) → T_{3}'
22. Vector(Q, Q + UnitVector[T_{1}']) → N_{1}
23. Vector(R, R + UnitVector[T_{2}']) → N_{2}
24. Vector(S, S + UnitVector[T_{3}']) → N_{3}
25. Vector(Q, Q + T_{1} ⊗ N_{1}) → B_{1}
26. Vector(R, R + T_{2} ⊗ N_{2}) → B_{2}
27. Vector(S, S + T_{3} ⊗ N_{3}) → B_{3}
28. CurveCartesian(r_{0}(((cbrt(2) * (sqrt((36 * s^(2)) + 2) + (6 * s))^(2 / 3)) - 2^(2 / 3)) / ((2 * cbrt(sqrt((36 * s^(2)) + 2) + (6 * s))))), s, -10, 10) → r_{3}