apps.dynamics

Newtons2nd

object Newtons2nd extends App

The Newtons2nd object is used to illustrate the RungeKutta (RK) and DormandPrince (DP) ODE solvers by applying them to Newton's Second Law of Motion, f = ma = -gm. The flight of a golf ball is simulated from impact until the ball hits the ground. Note, a more realistic simulation would take additional forces into account: drag, lift and spin.

See also

http://claymore.engineer.gvsu.edu/~lait/312/golfball.pdf The accurracies of RK and DP versus the exact solution (EX) are compared.

http://home2.fvcc.edu/~dhicketh/DiffEqns/Spring11projects/Brett_Burglund_Ryan_Street/Diff%20Q/pdfscreen/projectoutline.pdf

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  1. final def !=(arg0: AnyRef): Boolean

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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

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  4. final def ==(arg0: AnyRef): Boolean

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    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
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  6. val a: Double

  7. val aa: Double

  8. def args: Array[String]

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  9. final def asInstanceOf[T0]: T0

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  10. def clone(): AnyRef

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  11. def delayedInit(body: ⇒ Unit): Unit

    Definition Classes
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  12. val dt: Double

  13. def dx_dt(t: Double, x: Double): Double

  14. def dy_dt(t: Double, y: Double): Double

  15. final def eq(arg0: AnyRef): Boolean

    Definition Classes
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  16. def equals(arg0: Any): Boolean

    Definition Classes
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  17. def exactSolution(t: Double): VectorD

  18. val executionStart: Long

    Definition Classes
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  19. def finalize(): Unit

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  20. val g: Double

  21. final def getClass(): Class[_]

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  22. def hashCode(): Int

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  23. final def isInstanceOf[T0]: Boolean

    Definition Classes
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  24. val m: Double

  25. def main(args: Array[String]): Unit

    Definition Classes
    App

  26. val n: Int

  27. final def ne(arg0: AnyRef): Boolean

    Definition Classes
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  28. final def notify(): Unit

    Definition Classes
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  29. final def notifyAll(): Unit

    Definition Classes
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  30. val odes: Array[(Double, Double) ⇒ Double]

  31. val p0: VectorD

  32. val p_d: MatrixD

  33. val p_e: MatrixD

  34. val p_r: MatrixD

  35. val s: Double

  36. val sf: Double

  37. val ss: Double

  38. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
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  39. var t: Double

  40. val tm: Double

  41. def toString(): String

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  42. val tt: VectorD

  43. val v0: VectorD

  44. final def wait(): Unit

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  45. final def wait(arg0: Long, arg1: Int): Unit

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  46. final def wait(arg0: Long): Unit

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