#include #include #include #include #include #include #include namespace { const double PI = 3.14159265358979323; const double SOLAR_MASS = 4 * PI * PI; const double DAYS_PER_YEAR = 365.24; struct Body { std::vector r, v; double m; }; std::unordered_map BODIES = { {"sun", {{0.0, 0.0, 0.0}, {0.0, 0.0, 0.0}, SOLAR_MASS}}, {"jupiter", {{4.84143144246472090e+00, -1.16032004402742839e+00, -1.03622044471123109e-01}, {1.66007664274403694e-03 * DAYS_PER_YEAR, 7.69901118419740425e-03 * DAYS_PER_YEAR, -6.90460016972063023e-05 * DAYS_PER_YEAR}, 9.54791938424326609e-04 * SOLAR_MASS}}, {"saturn", {{8.34336671824457987e+00, 4.12479856412430479e+00, -4.03523417114321381e-01}, {-2.76742510726862411e-03 * DAYS_PER_YEAR, 4.99852801234917238e-03 * DAYS_PER_YEAR, 2.30417297573763929e-05 * DAYS_PER_YEAR}, 2.85885980666130812e-04 * SOLAR_MASS}}, {"uranus", {{1.28943695621391310e+01, -1.51111514016986312e+01, -2.23307578892655734e-01}, {2.96460137564761618e-03 * DAYS_PER_YEAR, 2.37847173959480950e-03 * DAYS_PER_YEAR, -2.96589568540237556e-05 * DAYS_PER_YEAR}, 4.36624404335156298e-05 * SOLAR_MASS}}, {"neptune", {{1.53796971148509165e+01, -2.59193146099879641e+01, 1.79258772950371181e-01}, {2.68067772490389322e-03 * DAYS_PER_YEAR, 1.62824170038242295e-03 * DAYS_PER_YEAR, -9.51592254519715870e-05 * DAYS_PER_YEAR}, 5.15138902046611451e-05 * SOLAR_MASS}}, }; template auto values(std::unordered_map &m) { std::vector v; v.reserve(m.size()); for (auto &e : m) v.push_back(&e.second); return v; } template auto combinations(const std::vector &v) { std::vector> p; auto n = v.size(); p.reserve(n); for (auto i = 0; i < n - 1; i++) for (auto j = i + 1; j < n; j++) p.push_back({v[i], v[j]}); return p; } std::vector SYSTEM = values(BODIES); auto PAIRS = combinations(SYSTEM); void advance(double dt, int n, std::vector &bodies = SYSTEM, std::vector> &pairs = PAIRS) { for (int i = 0; i < n; i++) { for (auto &pair : pairs) { double x1 = pair.first->r[0], y1 = pair.first->r[1], z1 = pair.first->r[2]; auto &v1 = pair.first->v; double m1 = pair.first->m; double x2 = pair.second->r[0], y2 = pair.second->r[1], z2 = pair.second->r[2]; auto &v2 = pair.second->v; double m2 = pair.second->m; double dx = x1 - x2, dy = y1 - y2, dz = z1 - z2; double mag = dt * std::pow((dx * dx + dy * dy + dz * dz), -1.5); double b1m = m1 * mag; double b2m = m2 * mag; v1[0] -= dx * b2m; v1[1] -= dy * b2m; v1[2] -= dz * b2m; v2[0] += dx * b1m; v2[1] += dy * b1m; v2[2] += dz * b1m; } for (auto *body : bodies) { auto &r = body->r; double vx = body->v[0], vy = body->v[1], vz = body->v[2]; r[0] += dt * vx; r[1] += dt * vy; r[2] += dt * vz; } } } void report_energy(std::vector &bodies = SYSTEM, std::vector> &pairs = PAIRS, double e = 0.0) { for (auto &pair : pairs) { double x1 = pair.first->r[0], y1 = pair.first->r[1], z1 = pair.first->r[2]; auto &v1 = pair.first->v; double m1 = pair.first->m; double x2 = pair.second->r[0], y2 = pair.second->r[1], z2 = pair.second->r[2]; auto &v2 = pair.second->v; double m2 = pair.second->m; double dx = x1 - x2, dy = y1 - y2, dz = z1 - z2; e -= (m1 * m2) / std::pow((dx * dx + dy * dy + dz * dz), 0.5); } for (auto *body : bodies) { double vx = body->v[0], vy = body->v[1], vz = body->v[2]; double m = body->m; e += m * (vx * vx + vy * vy + vz * vz) / 2.; } std::cout << e << std::endl; } void offset_momentum(Body &ref, std::vector &bodies = SYSTEM, double px = 0.0, double py = 0.0, double pz = 0.0) { for (auto *body : bodies) { double vx = body->v[0], vy = body->v[1], vz = body->v[2]; double m = body->m; px -= vx * m; py -= vy * m; pz -= vz * m; } auto &v = ref.v; double m = ref.m; v[0] = px / m; v[1] = py / m; v[2] = pz / m; } } // namespace int main(int argc, char *argv[]) { using clock = std::chrono::high_resolution_clock; using std::chrono::duration_cast; using std::chrono::milliseconds; auto t = clock::now(); std::string ref = "sun"; offset_momentum(BODIES[ref]); report_energy(); advance(0.01, std::atoi(argv[1])); report_energy(); std::cout << (duration_cast(clock::now() - t).count() / 1e3) << std::endl; }