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pse example 4.3 - the long jump.cpp
C++
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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); }
};
 
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)
{
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;
 
throw "exception";
}
 
int _tmain(int argc, _TCHAR* argv[])
{
// A long-jumper leaves the ground at an angle of 20.0° above
// the horizontal and at a speed of 11.0 m/s. (a) How far does
// he jump in the horizontal direction? (Assume his motion is
// equivalent to that of a particle.)
 
// For the purposes of solving the problem, let's take
// point A as the initial position
// point B as the peak position
// point C as the final position.
 
// First we'll get the answer in a symbolic form.
 
Obj objA; // An Obj representing the object at A
 
objA.position = Point(0, 0);
 
auto thA = Symbolic("thA"); // angle at point A
auto vA = Symbolic("vA"); // velocity at point A
 
objA.velocity = Point::FromAngle(thA, vA);
objA.acceleration = Point(0, -g);
objA.time = 0;
 
Obj objB;
 
// The horizontal velocity at B is the same as it is at A.
// The vertical velocity at B is 0;
 
objB.velocity = Point(objA.velocity.x, 0);
objB.acceleration = Point(0, -g);
 
auto timeB = CalcTime(objA, objB);
auto timeC = timeB * 2;
 
// Let's display the object at the three states, A, B, C:
 
cout << "object at point A:" << endl;
objA.Print();
cout << endl ;
 
cout << "object at point B:" << endl;
objA.AtTime(timeB).Print();
cout << endl;
 
cout << "object at point C:" << endl;
objA.AtTime(timeC).Print();
cout << endl;
// Now let's get the numerical answer.
 
// Subsitute the numerical values to get a numerical timeB value:
 
auto timeBNum = timeB[g==9.8, thA==Radians(20), vA==11][Pi==3.14159];
 
cout << "numerical time at B is ";
cout << timeBNum << endl << endl;
 
// Let's reassign some symbols to their numerical values:
 
Pi = 3.14159;
thA = Radians(20);
vA = 11;
g = 9.8;
 
// Re-run the calculation to get the numerical values.
 
objA.velocity = Point::FromAngle(thA, vA);
objA.acceleration = Point(0, -g);
 
cout << "object at point A (numerical): " << endl;
objA.AtTime(0).Print();
cout << endl;
 
cout << "object at point B (numerical): " << endl;
objA.AtTime(timeBNum).Print();
cout << endl;
 
cout << "object at point C (numerical): " << endl;
objA.AtTime(timeBNum*2).Print();
cout << endl;
 
cout << "How far does he dump in the horizontal direction?" << endl;
cout << objA.AtTime(timeBNum*2).position.x << endl << endl;
 
cout << "What is the maximum height reached?" << endl;
cout << objA.AtTime(timeBNum).position.y << endl;
 
system("pause");
return 0;
}

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