// xB = xA + vAx t + 1/2 ax t^2 (9)
// yB = yA + vAy t + 1/2 ay t^2 (10)
// xB - xA = d cos th (13)
// yB - yA = d sin th (14)
// ax = 0 (11)
// vAx = vA cos(thA) (6)
// vAy = vA sin(thA) (7)
// (9): xB = xA + vAx t + 1/2 ax t^2
// xB - xA = vAx t + 1/2 ax t^2 (9.1)
// (10): yB = yA + vAy t + 1/2 ay t^2
// yB - yA = vAy t + 1/2 ay t^2 (10.1)
// (13): xB - xA = d cos th
// /. (9.1) vAx t + 1/2 ax t^2 = d cos th
// /. (11) vAx t = d cos th
// t t = d cos(th) / vAx (13.1)
// (14): yB - yA = d sin th
// /. (10.1) vAy t + 1/2 ay t^2 = d sin th
// /. (13.1) vAy [d cos(th) / vAx] + 1/2 ay [d cos(th) / vAx]^2 = d sin th
// vAy / vAx d cos(th) + 1/2 ay [d cos(th) / vAx]^2 = d sin th
// 1/2 ay [d cos(th) / vAx]^2 = d sin th - vAy / vAx d cos(th)
// 1/2 ay [d cos(th) / vAx]^2 = d [sin(th) - vAy / vAx cos(th)]
// 1/2 ay d^2 [cos(th) / vAx]^2 = d [sin(th) - vAy / vAx cos(th)]
// 1/2 ay d [cos(th) / vAx]^2 = [sin(th) - vAy / vAx cos(th)]
// d = 2 [sin(th) - vAy / vAx cos(th)] [vAx / cos(th)]^2 / ay
// if vAy = 0 then it simplifies to:
// d = 2 sin(th) [vAx / cos(th)]^2 / ay
#endregion
public Point ProjectileInclineIntersection(MathObject theta)
{
if (theta != null &&
velocity.x != null &&
velocity.y != null &&
acceleration.y != null &&
acceleration.y != 0 &&
acceleration.y != 0.0)
{
var d =
2 * (Trig.Sin(theta) - velocity.y / velocity.x * Trig.Cos(theta))
* ((velocity.x / Trig.Cos(theta)) ^ 2)
/ acceleration.y;
return
(new Point(
position.x + d * Trig.Cos(theta),
position.y + d * Trig.Sin(theta)));
}
throw new Exception();
}
public MathObject ForceMagnitude(Point f)
{
// 2 unknown force magnitudes
// 0 unknown force angles
if (forces.Count(elt => elt.magnitude == null) == 2
&&
forces.Count(elt => elt.angle == null) == 0)
{
var otherUnknownForce = forces.Find(elt => elt != f && elt.magnitude == null);
var knownForces = new List <Point>(forces);
knownForces.Remove(f);
knownForces.Remove(otherUnknownForce);
var th1 = f.angle;
var th2 = otherUnknownForce.angle;
var result = -acceleration.y * mass * Trig.Cos(th2) + acceleration.x * mass * Trig.Sin(th2);
knownForces.ForEach(elt =>
{
result = result - elt.magnitude * Trig.Cos(elt.angle) * Trig.Sin(th2);
result = result + elt.magnitude * Trig.Sin(elt.angle) * Trig.Cos(th2);
});
result = result / (Trig.Cos(th1) * Trig.Sin(th2) - Trig.Sin(th1) * Trig.Cos(th2));
return(result);
}
// F1 = (m ay - F2 sin(th2) - F3 sin(th3) ...) / sin(th1)
if (f.angle != null
&&
Trig.Sin(f.angle) != 0
&&
Trig.Sin(f.angle) != 0.0
&&
forces.Count(elt => elt.magnitude == null) == 1
&&
forces.Count(elt => elt.angle == null) == 0
)
{
var otherForces = new List <Point>(forces);
otherForces.Remove(f);
var val = mass * acceleration.y;
otherForces.ForEach(force => val = val - force.magnitude * Trig.Sin(force.angle));
val = val / Trig.Sin(f.angle);
return(val);
}
// F1 = (m ax - F2 cos(th2) - F3 cos(th3) ...) / cos(th1)
if (f.angle != null
&&
Trig.Cos(f.angle) != 0
&&
Trig.Cos(f.angle) != 0.0
&&
forces.Count(elt => elt.magnitude == null) == 1
&&
forces.Count(elt => elt.angle == null) == 0
)
{
var otherForces = new List <Point>(forces);
otherForces.Remove(f);
var val = mass * acceleration.x;
otherForces.ForEach(force => val = val - force.magnitude * Trig.Cos(force.angle));
val = val / Trig.Cos(f.angle);
return(val);
}
throw new Exception();
}
//////////////////////////////////////////////////////////////////////
public static Point FromAngle(MathObject angle, MathObject mag)
{
return(new Point(Trig.Cos(angle) * mag, Trig.Sin(angle) * mag));
}