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December 3, 2012 06:18
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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); } | |
}; | |
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 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"; | |
} | |
auto _g = Point(0, -g); | |
int _tmain(int argc, _TCHAR* argv[]) | |
{ | |
// A ski jumper leaves the ski track moving in the horizontal direction | |
// with a speed of 25.0 m/s, as shown in Figure 4.14. | |
// The landing incline below him falls off with a slope of 35.0°. | |
// Where does he land on the incline? | |
{ | |
Obj objA; | |
Obj objB; | |
auto xB = Symbolic("xB"); | |
auto yB = Symbolic("yB"); | |
auto th = Radians(35)[Pi == 3.14159]; | |
objA.time = 0; | |
objA.position.x = 0; | |
objA.position.y = 0; | |
objA.velocity.x = 25; | |
objA.velocity.y = 0; | |
_g = Point(0, -9.8); | |
objA.acceleration = _g; | |
/* | |
tan(th) = (yA - yB) / xB | |
yA = 0 tan(th) = (0 - yB) / xB | |
tan(th) = - yB / xB | |
yB = - xB tan(th) | |
*/ | |
objB.position.y = - xB * tan(th); | |
objB.velocity.x = objA.velocity.x; | |
objB.acceleration = _g; | |
auto timeB = CalcTime(objA, objB, 1); | |
cout << "time at B: " << timeB << endl; | |
objB = objA.AtTime(timeB); | |
cout << "xB = " << objB.position.x << " (1)" << endl; | |
cout << "yB = " << objB.position.y << " (2)" << endl; | |
cout << endl; | |
/* | |
xB = 9.45051 xB^(1/2) | |
xB^2 = 9.45051^2 xB | |
xB = 9.45051^2 | |
*/ | |
cout << "solve (1) for xB:" << endl; | |
objB.position.x = (objB.position.x^2) / xB; | |
cout << "xB = " << objB.position.x << " (1.1)" << endl; | |
cout << "replace in yB using (1.1)" << endl; | |
objB.position.y = objB.position.y[xB == objB.position.x]; | |
cout << "yB = " << objB.position.y << endl; | |
cout << "Determine how long the jumper is airborne" << endl; | |
timeB = timeB[xB == objB.position.x]; | |
cout << timeB << endl; | |
cout << "vertical component of velocity just before he lands:" << endl; | |
cout << objA.AtTime(timeB).velocity.y << endl; | |
} | |
system("pause"); | |
return 0; | |
} |
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