Task: Orbital elements
C: #include <stdio.h>
#include <math.h>

typedef struct {
    double x, y, z;
} vector;

vector add(vector v, vector w) {
    return (vector){v.x + w.x, v.y + w.y, v.z + w.z};
}

vector mul(vector v, double m) {
    return (vector){v.x * m, v.y * m, v.z * m};
}

vector div(vector v, double d) {
    return mul(v, 1.0 / d);
}

double vabs(vector v) {
    return sqrt(v.x * v.x + v.y * v.y + v.z * v.z);
}

vector mulAdd(vector v1, vector v2, double x1, double x2) {
    return add(mul(v1, x1), mul(v2, x2)); 
}

void vecAsStr(char buffer[], vector v) {
    sprintf(buffer, "(%.17g, %.17g, %.17g)", v.x, v.y, v.z);
}

void rotate(vector i, vector j, double alpha, vector ps[]) {
    ps[0] = mulAdd(i, j, cos(alpha), sin(alpha));
    ps[1] = mulAdd(i, j, -sin(alpha), cos(alpha));
}
 
void orbitalStateVectors(
    double semimajorAxis, double eccentricity, double inclination,
    double longitudeOfAscendingNode, double argumentOfPeriapsis,
    double trueAnomaly, vector ps[]) {

    vector i = {1.0, 0.0, 0.0};
    vector j = {0.0, 1.0, 0.0};
    vector k = {0.0, 0.0, 1.0};
    double l = 2.0, c, s, r, rprime;
    vector qs[2];
    rotate(i, j, longitudeOfAscendingNode, qs);
    i = qs[0]; j = qs[1];
    rotate(j, k, inclination, qs);
    j = qs[0];
    rotate(i, j, argumentOfPeriapsis, qs);
    i = qs[0]; j = qs[1];
    if (eccentricity != 1.0)  l = 1.0 - eccentricity * eccentricity;
    l *= semimajorAxis;
    c = cos(trueAnomaly);
    s = sin(trueAnomaly);
    r = l / (1.0 + eccentricity * c);
    rprime = s * r * r / l;
    ps[0] = mulAdd(i, j, c, s);
    ps[0] = mul(ps[0], r);
    ps[1] = mulAdd(i, j, rprime * c - r * s, rprime * s + r * c);
    ps[1] = div(ps[1], vabs(ps[1]));
    ps[1] = mul(ps[1], sqrt(2.0 / r - 1.0 / semimajorAxis));
}

int main() {
    double longitude = 355.0 / (113.0 * 6.0);
    vector ps[2];
    char buffer[80];
    orbitalStateVectors(1.0, 0.1, 0.0, longitude, 0.0, 0.0, ps);
    vecAsStr(buffer, ps[0]);
    printf("Position : %s\n", buffer);
    vecAsStr(buffer, ps[1]);
    printf("Speed    : %s\n", buffer);
    return 0;
}

C++: #include <iostream>
#include <tuple>

class Vector {
private:
    double _x, _y, _z;

public:
    Vector(double x, double y, double z) : _x(x), _y(y), _z(z) {
        
    }

    double getX() {
        return _x;
    }

    double getY() {
        return _y;
    }

    double getZ() {
        return _z;
    }

    double abs() {
        return sqrt(_x * _x + _y * _y + _z * _z);
    }

    Vector operator+(const Vector& rhs) const {
        return Vector(_x + rhs._x, _y + rhs._y, _z + rhs._z);
    }

    Vector operator*(double m) const {
        return Vector(_x * m, _y * m, _z * m);
    }

    Vector operator/(double m) const {
        return Vector(_x / m, _y / m, _z / m);
    }

    friend std::ostream& operator<<(std::ostream& os, const Vector& v);
};

std::ostream& operator<<(std::ostream& os, const Vector& v) {
    return os << '(' << v._x << ", " << v._y << ", " << v._z << ')';
}

std::pair<Vector, Vector> orbitalStateVectors(
    double semiMajorAxis,
    double eccentricity,
    double inclination,
    double longitudeOfAscendingNode,
    double argumentOfPeriapsis,
    double trueAnomaly
) {
    auto mulAdd = [](const Vector& v1, double x1, const Vector& v2, double x2) {
        return v1 * x1 + v2 * x2;
    };

    auto rotate = [mulAdd](const Vector& iv, const Vector& jv, double alpha) {
        return std::make_pair(
            mulAdd(iv, +cos(alpha), jv, sin(alpha)),
            mulAdd(iv, -sin(alpha), jv, cos(alpha))
        );
    };

    Vector i(1, 0, 0);
    Vector j(0, 1, 0);
    Vector k(0, 0, 1);

    auto p = rotate(i, j, longitudeOfAscendingNode);
    i = p.first; j = p.second;
    p = rotate(j, k, inclination);
    j = p.first;
    p = rotate(i, j, argumentOfPeriapsis);
    i = p.first; j = p.second;

    auto l = semiMajorAxis * ((eccentricity == 1.0) ? 2.0 : (1.0 - eccentricity * eccentricity));
    auto c = cos(trueAnomaly);
    auto s = sin(trueAnomaly);
    auto r = l / (1.0 + eccentricity * c);;
    auto rprime = s * r * r / l;
    auto position = mulAdd(i, c, j, s) * r;
    auto speed = mulAdd(i, rprime * c - r * s, j, rprime * s + r * c);
    speed = speed / speed.abs();
    speed = speed * sqrt(2.0 / r - 1.0 / semiMajorAxis);

    return std::make_pair(position, speed);
}

int main() {
    auto res = orbitalStateVectors(1.0, 0.1, 0.0, 355.0 / (113.0 * 6.0), 0.0, 0.0);
    std::cout << "Position : " << res.first << '\n';
    std::cout << "Speed    : " << res.second << '\n';

    return 0;
}