Created
December 8, 2012 23:37
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#include "stdafx.h" | |
#include "..\..\include\symbolicc++.h" | |
Symbolic Pi = "Pi"; | |
Symbolic g = "g"; | |
Symbolic Radians(Symbolic n) { return n * Pi / 180; } | |
Symbolic Degrees(Symbolic n) { return 180 * n / Pi; } | |
class Point | |
{ | |
public: | |
Symbolic x; | |
Symbolic y; | |
Point() { x = "NOTSET" ; y = "NOTSET"; } | |
Point(Symbolic x_val, Symbolic y_val) | |
{ | |
x = x_val; | |
y = y_val; | |
} | |
void Print() | |
{ | |
cout << "Point(" << x << ", " << y << ")"; | |
} | |
static Point FromAngle(Symbolic angle, Symbolic mag) | |
{ return Point(cos(angle) * mag, sin(angle) * mag); } | |
Point operator+(Point p) { return Point(x + p.x, y + p.y); } | |
Point operator*(Symbolic sym) { return Point(x * sym, y * sym); } | |
Point operator/(Symbolic sym) { return Point(x / sym, y / sym); } | |
Symbolic Norm() { return sqrt(x*x + y*y); } | |
double ToAngle() { return atan2(y, x); } | |
}; | |
void Unset(Symbolic &sym) { sym = "NOTSET"; } | |
bool IsSet(Symbolic sym) | |
{ | |
if (sym == "NOTSET") | |
return false; | |
else | |
return true; | |
} | |
bool HasVal(Symbolic sym) | |
{ | |
if (sym == "NOTSET") | |
return false; | |
else | |
return true; | |
} | |
class Obj | |
{ | |
public: | |
Point position, velocity, acceleration; | |
Symbolic speed; | |
Symbolic time; | |
void Print() | |
{ | |
// cout << "Obj:" << endl; | |
cout << "time: " << time << endl; | |
cout << "position.x: " << position.x << endl; | |
cout << "position.y: " << position.y << endl; | |
cout << "velocity.x: " << velocity.x << endl; | |
cout << "velocity.y: " << velocity.y << endl; | |
cout << "acceleration.x: " << acceleration.x << endl; | |
cout << "acceleration.y: " << acceleration.y << endl; | |
} | |
Obj AtTime(Symbolic t) | |
{ | |
Obj obj; | |
obj.time = t; | |
auto dt = t - time; | |
obj.acceleration = acceleration; | |
obj.velocity = velocity + acceleration * dt; | |
obj.position = position + velocity * dt + acceleration * dt * dt / 2; | |
return obj; | |
} | |
}; | |
Symbolic CalcTime(Obj& a, Obj& b, int flag=0) | |
{ | |
if (HasVal(b.velocity.x) && | |
HasVal(a.velocity.x) && | |
HasVal(a.acceleration.x) && | |
a.acceleration.x != 0.0 && | |
a.acceleration.x != 0) | |
return (b.velocity.x - a.velocity.x) / a.acceleration.x; | |
if (HasVal(b.velocity.y) && | |
HasVal(a.velocity.y) && | |
HasVal(a.acceleration.y) && | |
a.acceleration.y != 0.0 && | |
a.acceleration.y != 0) | |
return (b.velocity.y - a.velocity.y) / a.acceleration.y; | |
if (HasVal(a.position.x) && | |
HasVal(b.position.x) && | |
HasVal(a.velocity.x) && | |
a.velocity.x != 0 && | |
a.velocity.x != 0.0) | |
return (b.position.x - a.position.x) / a.velocity.x; | |
if (HasVal(b.position.x) && | |
HasVal(a.position.x) && | |
HasVal(a.velocity.x) && | |
HasVal(a.acceleration.x) && | |
a.acceleration.x != 0 && | |
a.acceleration.x != 0.0) | |
{ | |
if (flag == 0) | |
return | |
(-a.velocity.x + sqrt(pow(a.velocity.x, Symbolic(2)) - 2 * a.acceleration.x * (a.position.x - b.position.x))) | |
/ | |
a.acceleration.x; | |
else | |
return | |
(-a.velocity.x - sqrt(pow(a.velocity.x, Symbolic(2)) - 2 * a.acceleration.x * (a.position.x - b.position.x))) | |
/ | |
a.acceleration.x; | |
} | |
if (HasVal(a.position.y) && | |
HasVal(b.position.y) && | |
HasVal(a.velocity.y) && | |
HasVal(a.acceleration.y) && | |
a.acceleration.y != 0 && | |
a.acceleration.y != 0.0) | |
{ | |
if (flag == 0) | |
return | |
(-a.velocity.y + sqrt(pow(a.velocity.y, Symbolic(2)) - 2 * a.acceleration.y * (a.position.y - b.position.y))) | |
/ | |
a.acceleration.y; | |
else | |
return | |
(-a.velocity.y - sqrt(pow(a.velocity.y, Symbolic(2)) - 2 * a.acceleration.y * (a.position.y - b.position.y))) | |
/ | |
a.acceleration.y; | |
} | |
throw "exception"; | |
} | |
Symbolic CalcInitialVelocityX(Obj& a, Obj& b) | |
{ | |
if (HasVal(a.position.x) && | |
HasVal(a.position.y) && | |
HasVal(a.time) && | |
HasVal(b.time) && | |
HasVal(a.acceleration.x)) | |
{ | |
auto dt = b.time - a.time; | |
return (b.position.x - a.position.x - a.acceleration.x * dt^2 / 2) / dt; | |
} | |
throw "exception"; | |
} | |
auto _g = Point(0, -g); | |
double SymmetricalAbout(double a, double b) { return a + a - b; } | |
// sin(a th) = b | |
Symbolic SineCalcTheta(Symbolic a, Symbolic b, int solution = 0, int n = 0) | |
{ | |
if (solution == 0) return (- asin(b) + 2 * Pi * n + Pi) / a; | |
if (solution == 1) return (asin(b) + 2 * Pi * n) / a; | |
} | |
Symbolic CalcInitialAngle(Obj a, Obj b, int sol = 0, int n = 0) | |
{ | |
if (HasVal(a.position.x) && | |
HasVal(b.position.x) && | |
HasVal(a.acceleration.y) && | |
HasVal(a.speed)) | |
if (sol == 0) | |
return (- asin(- a.acceleration.y * (b.position.x - a.position.x) / (a.speed^2)) + 2 * Pi * n + Pi) / 2; | |
if (sol == 1) | |
return (asin(- a.acceleration.y * (b.position.x - a.position.x) / (a.speed^2)) + 2 * Pi * n) / 2; | |
throw "exception"; | |
} | |
int _tmain(int argc, _TCHAR* argv[]) | |
{ | |
// A projectile is fired in such a way that its horizontal | |
// range is equal to three times its maximum height. | |
// | |
// What is the angle of projection? | |
// | |
// Give your answer to three significant figures. | |
{ | |
Obj objA; | |
auto vxA = Symbolic("vxA"); | |
auto vyA = Symbolic("vyA"); | |
objA.time = 0; | |
objA.position = Point(0, 0); | |
objA.velocity = Point(vxA, vyA); | |
objA.acceleration = _g; | |
Obj objB; | |
objB.velocity.y = 0; | |
objB.acceleration = _g; | |
auto timeAB = CalcTime(objA, objB); | |
auto timeB = objA.time + timeAB; | |
objB = objA.AtTime(timeB); | |
auto timeC = timeB*2; | |
auto objC = objA.AtTime(timeC); | |
cout << "maximum height is " << objB.position.y << endl; | |
cout << "horizontal range is " << objC.position.x << endl; | |
// H = 1/2 vyA^2 / g | |
// R = 2 vxA vyA / g | |
// | |
// "its horizontal range is equal to three times its maximum height" | |
// | |
// R = 3 H | |
// | |
// 2 vxA vyA / g = 3 1/2 vyA^2 / g | |
// | |
// 4 vxA = 3 vyA | |
// | |
// vxA = vA cos(th) | |
// vyA = vA sin(th) | |
// | |
// 4 vA cos(th) = 3 vA sin(th) | |
// | |
// 4 cos(th) = 3 sin(th) | |
// | |
// 4/3 = tan(th) | |
} | |
system("pause"); | |
return 0; | |
} |
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