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;
}

Python: import math

class Vector:
    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

    def __add__(self, other):
        return Vector(self.x + other.x, self.y + other.y, self.z + other.z)

    def __mul__(self, other):
        return Vector(self.x * other, self.y * other, self.z * other)

    def __div__(self, other):
        return Vector(self.x / other, self.y / other, self.z / other)

    def __str__(self):
        return '({x}, {y}, {z})'.format(x=self.x, y=self.y, z=self.z)

    def abs(self):
        return math.sqrt(self.x*self.x + self.y*self.y + self.z*self.z)

def mulAdd(v1, x1, v2, x2):
    return v1 * x1 + v2 * x2

def rotate(i, j, alpha):
    return [mulAdd(i,math.cos(alpha),j,math.sin(alpha)), mulAdd(i,-math.sin(alpha),j,math.cos(alpha))]

def orbitalStateVectors(semimajorAxis, eccentricity, inclination, longitudeOfAscendingNode, argumentOfPeriapsis, trueAnomaly):
    i = Vector(1, 0, 0)
    j = Vector(0, 1, 0)
    k = Vector(0, 0, 1)

    p = rotate(i, j, longitudeOfAscendingNode)
    i = p[0]
    j = p[1]
    p = rotate(j, k, inclination)
    j = p[0]
    p  =rotate(i, j, argumentOfPeriapsis)
    i = p[0]
    j = p[1]

    l = 2.0 if (eccentricity == 1.0) else 1.0 - eccentricity * eccentricity
    l *= semimajorAxis
    c = math.cos(trueAnomaly)
    s = math.sin(trueAnomaly)
    r = 1 / (1.0 + eccentricity * c)
    rprime = s * r * r / l
    position = mulAdd(i, c, j, s) * r
    speed = mulAdd(i, rprime * c - r * s, j, rprime * s + r * c)
    speed = speed / speed.abs()
    speed = speed * math.sqrt(2.0 / r - 1.0 / semimajorAxis)

    return [position, speed]

ps = orbitalStateVectors(1.0, 0.1, 0.0, 355.0 / (113.0 * 6.0), 0.0, 0.0)
print "Position :", ps[0]
print "Speed    :", ps[1]