C5 DETEST
Equations:
$$\begin{align}\dot{x}_{0}&=x_{1}\\\dot{x}_{1}&=- \frac{1.00096076292 \cdot x_{0}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{2}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{4}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{6}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{8}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(- x_{0} + x_{2}\right)}{\left(\left(- x_{0} + x_{2}\right)^{2} + \left(- x_{10} + x_{12}\right)^{2} + \left(- x_{20} + x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{0} + x_{4}\right)}{\left(\left(- x_{0} + x_{4}\right)^{2} + \left(- x_{10} + x_{14}\right)^{2} + \left(- x_{20} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{0} + x_{6}\right)}{\left(\left(- x_{0} + x_{6}\right)^{2} + \left(- x_{10} + x_{16}\right)^{2} + \left(- x_{20} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{0} + x_{8}\right)}{\left(\left(- x_{0} + x_{8}\right)^{2} + \left(- x_{10} + x_{18}\right)^{2} + \left(- x_{20} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{2}&=x_{3}\\\dot{x}_{3}&=- \frac{0.0009547861 \cdot x_{0}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{1.00029156055 \cdot x_{2}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{4}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{6}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{8}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{0} - x_{2}\right)}{\left(\left(x_{0} - x_{2}\right)^{2} + \left(x_{10} - x_{12}\right)^{2} + \left(x_{20} - x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{2} + x_{4}\right)}{\left(\left(- x_{12} + x_{14}\right)^{2} + \left(- x_{2} + x_{4}\right)^{2} + \left(- x_{22} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{2} + x_{6}\right)}{\left(\left(- x_{12} + x_{16}\right)^{2} + \left(- x_{2} + x_{6}\right)^{2} + \left(- x_{22} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{2} + x_{8}\right)}{\left(\left(- x_{12} + x_{18}\right)^{2} + \left(- x_{2} + x_{8}\right)^{2} + \left(- x_{22} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{4}&=x_{5}\\\dot{x}_{5}&=- \frac{0.0009547861 \cdot x_{0}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{2}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{1.00004970413 \cdot x_{4}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{6}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{8}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{0} - x_{4}\right)}{\left(\left(x_{0} - x_{4}\right)^{2} + \left(x_{10} - x_{14}\right)^{2} + \left(x_{20} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{2} - x_{4}\right)}{\left(\left(x_{12} - x_{14}\right)^{2} + \left(x_{2} - x_{4}\right)^{2} + \left(x_{22} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{4} + x_{6}\right)}{\left(\left(- x_{14} + x_{16}\right)^{2} + \left(- x_{24} + x_{26}\right)^{2} + \left(- x_{4} + x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{4} + x_{8}\right)}{\left(\left(- x_{14} + x_{18}\right)^{2} + \left(- x_{24} + x_{28}\right)^{2} + \left(- x_{4} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{6}&=x_{7}\\\dot{x}_{7}&=- \frac{0.0009547861 \cdot x_{0}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{2}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{4}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{1.00005775273 \cdot x_{6}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{8}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{0} - x_{6}\right)}{\left(\left(x_{0} - x_{6}\right)^{2} + \left(x_{10} - x_{16}\right)^{2} + \left(x_{20} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{2} - x_{6}\right)}{\left(\left(x_{12} - x_{16}\right)^{2} + \left(x_{2} - x_{6}\right)^{2} + \left(x_{22} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{4} - x_{6}\right)}{\left(\left(x_{14} - x_{16}\right)^{2} + \left(x_{24} - x_{26}\right)^{2} + \left(x_{4} - x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{6} + x_{8}\right)}{\left(\left(- x_{16} + x_{18}\right)^{2} + \left(- x_{26} + x_{28}\right)^{2} + \left(- x_{6} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{8}&=x_{9}\\\dot{x}_{9}&=- \frac{0.0009547861 \cdot x_{0}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{2}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{4}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{6}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{1.00000875459 \cdot x_{8}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{0} - x_{8}\right)}{\left(\left(x_{0} - x_{8}\right)^{2} + \left(x_{10} - x_{18}\right)^{2} + \left(x_{20} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{2} - x_{8}\right)}{\left(\left(x_{12} - x_{18}\right)^{2} + \left(x_{2} - x_{8}\right)^{2} + \left(x_{22} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{4} - x_{8}\right)}{\left(\left(x_{14} - x_{18}\right)^{2} + \left(x_{24} - x_{28}\right)^{2} + \left(x_{4} - x_{8}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(x_{6} - x_{8}\right)}{\left(\left(x_{16} - x_{18}\right)^{2} + \left(x_{26} - x_{28}\right)^{2} + \left(x_{6} - x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{10}&=x_{11}\\\dot{x}_{11}&=- \frac{1.00096076292 \cdot x_{10}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{12}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{14}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{16}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{18}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(- x_{10} + x_{12}\right)}{\left(\left(- x_{0} + x_{2}\right)^{2} + \left(- x_{10} + x_{12}\right)^{2} + \left(- x_{20} + x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{10} + x_{14}\right)}{\left(\left(- x_{0} + x_{4}\right)^{2} + \left(- x_{10} + x_{14}\right)^{2} + \left(- x_{20} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{10} + x_{16}\right)}{\left(\left(- x_{0} + x_{6}\right)^{2} + \left(- x_{10} + x_{16}\right)^{2} + \left(- x_{20} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{10} + x_{18}\right)}{\left(\left(- x_{0} + x_{8}\right)^{2} + \left(- x_{10} + x_{18}\right)^{2} + \left(- x_{20} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{12}&=x_{13}\\\dot{x}_{13}&=- \frac{0.0009547861 \cdot x_{10}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{1.00029156055 \cdot x_{12}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{14}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{16}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{18}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{10} - x_{12}\right)}{\left(\left(x_{0} - x_{2}\right)^{2} + \left(x_{10} - x_{12}\right)^{2} + \left(x_{20} - x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{12} + x_{14}\right)}{\left(\left(- x_{12} + x_{14}\right)^{2} + \left(- x_{2} + x_{4}\right)^{2} + \left(- x_{22} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{12} + x_{16}\right)}{\left(\left(- x_{12} + x_{16}\right)^{2} + \left(- x_{2} + x_{6}\right)^{2} + \left(- x_{22} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{12} + x_{18}\right)}{\left(\left(- x_{12} + x_{18}\right)^{2} + \left(- x_{2} + x_{8}\right)^{2} + \left(- x_{22} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{14}&=x_{15}\\\dot{x}_{15}&=- \frac{0.0009547861 \cdot x_{10}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{12}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{1.00004970413 \cdot x_{14}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{16}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{18}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{10} - x_{14}\right)}{\left(\left(x_{0} - x_{4}\right)^{2} + \left(x_{10} - x_{14}\right)^{2} + \left(x_{20} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{12} - x_{14}\right)}{\left(\left(x_{12} - x_{14}\right)^{2} + \left(x_{2} - x_{4}\right)^{2} + \left(x_{22} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{14} + x_{16}\right)}{\left(\left(- x_{14} + x_{16}\right)^{2} + \left(- x_{24} + x_{26}\right)^{2} + \left(- x_{4} + x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{14} + x_{18}\right)}{\left(\left(- x_{14} + x_{18}\right)^{2} + \left(- x_{24} + x_{28}\right)^{2} + \left(- x_{4} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{16}&=x_{17}\\\dot{x}_{17}&=- \frac{0.0009547861 \cdot x_{10}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{12}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{14}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{1.00005775273 \cdot x_{16}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{18}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{10} - x_{16}\right)}{\left(\left(x_{0} - x_{6}\right)^{2} + \left(x_{10} - x_{16}\right)^{2} + \left(x_{20} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{12} - x_{16}\right)}{\left(\left(x_{12} - x_{16}\right)^{2} + \left(x_{2} - x_{6}\right)^{2} + \left(x_{22} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{14} - x_{16}\right)}{\left(\left(x_{14} - x_{16}\right)^{2} + \left(x_{24} - x_{26}\right)^{2} + \left(x_{4} - x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{16} + x_{18}\right)}{\left(\left(- x_{16} + x_{18}\right)^{2} + \left(- x_{26} + x_{28}\right)^{2} + \left(- x_{6} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{18}&=x_{19}\\\dot{x}_{19}&=- \frac{0.0009547861 \cdot x_{10}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{12}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{14}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{16}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{1.00000875459 \cdot x_{18}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{10} - x_{18}\right)}{\left(\left(x_{0} - x_{8}\right)^{2} + \left(x_{10} - x_{18}\right)^{2} + \left(x_{20} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{12} - x_{18}\right)}{\left(\left(x_{12} - x_{18}\right)^{2} + \left(x_{2} - x_{8}\right)^{2} + \left(x_{22} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{14} - x_{18}\right)}{\left(\left(x_{14} - x_{18}\right)^{2} + \left(x_{24} - x_{28}\right)^{2} + \left(x_{4} - x_{8}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(x_{16} - x_{18}\right)}{\left(\left(x_{16} - x_{18}\right)^{2} + \left(x_{26} - x_{28}\right)^{2} + \left(x_{6} - x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{20}&=x_{21}\\\dot{x}_{21}&=- \frac{1.00096076292 \cdot x_{20}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{22}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{24}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{26}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{28}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(- x_{20} + x_{22}\right)}{\left(\left(- x_{0} + x_{2}\right)^{2} + \left(- x_{10} + x_{12}\right)^{2} + \left(- x_{20} + x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{20} + x_{24}\right)}{\left(\left(- x_{0} + x_{4}\right)^{2} + \left(- x_{10} + x_{14}\right)^{2} + \left(- x_{20} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{20} + x_{26}\right)}{\left(\left(- x_{0} + x_{6}\right)^{2} + \left(- x_{10} + x_{16}\right)^{2} + \left(- x_{20} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{20} + x_{28}\right)}{\left(\left(- x_{0} + x_{8}\right)^{2} + \left(- x_{10} + x_{18}\right)^{2} + \left(- x_{20} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{22}&=x_{23}\\\dot{x}_{23}&=- \frac{0.0009547861 \cdot x_{20}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{1.00029156055 \cdot x_{22}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{24}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{26}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{28}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{20} - x_{22}\right)}{\left(\left(x_{0} - x_{2}\right)^{2} + \left(x_{10} - x_{12}\right)^{2} + \left(x_{20} - x_{22}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(- x_{22} + x_{24}\right)}{\left(\left(- x_{12} + x_{14}\right)^{2} + \left(- x_{2} + x_{4}\right)^{2} + \left(- x_{22} + x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{22} + x_{26}\right)}{\left(\left(- x_{12} + x_{16}\right)^{2} + \left(- x_{2} + x_{6}\right)^{2} + \left(- x_{22} + x_{26}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{22} + x_{28}\right)}{\left(\left(- x_{12} + x_{18}\right)^{2} + \left(- x_{2} + x_{8}\right)^{2} + \left(- x_{22} + x_{28}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{24}&=x_{25}\\\dot{x}_{25}&=- \frac{0.0009547861 \cdot x_{20}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{22}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{1.00004970413 \cdot x_{24}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{26}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{28}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{20} - x_{24}\right)}{\left(\left(x_{0} - x_{4}\right)^{2} + \left(x_{10} - x_{14}\right)^{2} + \left(x_{20} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{22} - x_{24}\right)}{\left(\left(x_{12} - x_{14}\right)^{2} + \left(x_{2} - x_{4}\right)^{2} + \left(x_{22} - x_{24}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(- x_{24} + x_{26}\right)}{\left(\left(- x_{14} + x_{16}\right)^{2} + \left(- x_{24} + x_{26}\right)^{2} + \left(- x_{4} + x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{24} + x_{28}\right)}{\left(\left(- x_{14} + x_{18}\right)^{2} + \left(- x_{24} + x_{28}\right)^{2} + \left(- x_{4} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{26}&=x_{27}\\\dot{x}_{27}&=- \frac{0.0009547861 \cdot x_{20}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{22}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{24}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{1.00005775273 \cdot x_{26}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{2.77777 \cdot 10^{-6} \cdot x_{28}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{20} - x_{26}\right)}{\left(\left(x_{0} - x_{6}\right)^{2} + \left(x_{10} - x_{16}\right)^{2} + \left(x_{20} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{22} - x_{26}\right)}{\left(\left(x_{12} - x_{16}\right)^{2} + \left(x_{2} - x_{6}\right)^{2} + \left(x_{22} - x_{26}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{24} - x_{26}\right)}{\left(\left(x_{14} - x_{16}\right)^{2} + \left(x_{24} - x_{26}\right)^{2} + \left(x_{4} - x_{6}\right)^{2}\right)^{3 / 2}} + \frac{2.77777 \cdot 10^{-6} \cdot \left(- x_{26} + x_{28}\right)}{\left(\left(- x_{16} + x_{18}\right)^{2} + \left(- x_{26} + x_{28}\right)^{2} + \left(- x_{6} + x_{8}\right)^{2}\right)^{3 / 2}}\\\dot{x}_{28}&=x_{29}\\\dot{x}_{29}&=- \frac{0.0009547861 \cdot x_{20}}{\left(x_{0}^{2} + x_{10}^{2} + x_{20}^{2}\right)^{3 / 2}} - \frac{0.00028558373 \cdot x_{22}}{\left(x_{12}^{2} + x_{2}^{2} + x_{22}^{2}\right)^{3 / 2}} - \frac{4.372731 \cdot 10^{-5} \cdot x_{24}}{\left(x_{14}^{2} + x_{24}^{2} + x_{4}^{2}\right)^{3 / 2}} - \frac{5.177591 \cdot 10^{-5} \cdot x_{26}}{\left(x_{16}^{2} + x_{26}^{2} + x_{6}^{2}\right)^{3 / 2}} - \frac{1.00000875459 \cdot x_{28}}{\left(x_{18}^{2} + x_{28}^{2} + x_{8}^{2}\right)^{3 / 2}} + \frac{0.0009547861 \cdot \left(x_{20} - x_{28}\right)}{\left(\left(x_{0} - x_{8}\right)^{2} + \left(x_{10} - x_{18}\right)^{2} + \left(x_{20} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{0.00028558373 \cdot \left(x_{22} - x_{28}\right)}{\left(\left(x_{12} - x_{18}\right)^{2} + \left(x_{2} - x_{8}\right)^{2} + \left(x_{22} - x_{28}\right)^{2}\right)^{3 / 2}} + \frac{4.372731 \cdot 10^{-5} \cdot \left(x_{24} - x_{28}\right)}{\left(\left(x_{14} - x_{18}\right)^{2} + \left(x_{24} - x_{28}\right)^{2} + \left(x_{4} - x_{8}\right)^{2}\right)^{3 / 2}} + \frac{5.177591 \cdot 10^{-5} \cdot \left(x_{26} - x_{28}\right)}{\left(\left(x_{16} - x_{18}\right)^{2} + \left(x_{26} - x_{28}\right)^{2} + \left(x_{6} - x_{8}\right)^{2}\right)^{3 / 2}}\end{align}$$
Description:
Derived from the five body problem: the motion of 5 outer planets about the sun.
Link to DETEST description
Keywords:
chaotic; min test set
Plots:
Initial value problems:
IVP 116
Class: PINLCNU
Initial conditions:
$$\begin{align}x_{0}(0)&=3.4294741518\\x_{1}(0)&=-0.5571605704\\x_{2}(0)&=6.6414554255\\x_{3}(0)&=-0.4155707763\\x_{4}(0)&=11.2630437207\\x_{5}(0)&=-0.3253256691\\x_{6}(0)&=-30.1552268759\\x_{7}(0)&=-0.0240476254\\x_{8}(0)&=-21.123835338\\x_{9}(0)&=-0.1768607531\\x_{10}(0)&=3.3538695971\\x_{11}(0)&=0.5056967832\\x_{12}(0)&=5.9715695787\\x_{13}(0)&=0.3656827228\\x_{14}(0)&=14.6952576794\\x_{15}(0)&=0.1897060219\\x_{16}(0)&=1.656999664\\x_{17}(0)&=-0.2876595326\\x_{18}(0)&=28.4465098142\\x_{19}(0)&=-0.216393453\\x_{20}(0)&=1.3549401715\\x_{21}(0)&=0.2305785439\\x_{22}(0)&=2.1823149972\\x_{23}(0)&=0.1691432132\\x_{24}(0)&=6.2796052506\\x_{25}(0)&=0.0877265322\\x_{26}(0)&=1.4378575272\\x_{27}(0)&=-0.1172195431\\x_{28}(0)&=15.3882659679\\x_{29}(0)&=-0.0148647893\end{align}$$
Exact Solution*:
No exact solution provided.
View test data:
- method: HOE
- order: 10
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=0.33780
- c5: t_us=0.33100 , e_us=9.887923813067800e-17
- c6: t_bd=10.000000 , e_bd=2.161465451067102e-15
- method: HOE
- order: 15
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=0.69260
- c5: t_us=0.67790 , e_us=1.040834085586084e-17
- c6: t_bd=10.000000 , e_bd=2.359223927328458e-16
- method: HOE
- order: 20
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=1.57810
- c5: t_us=1.55500 , e_us=1.908195823574488e-17
- c6: t_bd=10.000000 , e_bd=1.526556658859590e-16
- method: HOE
- order: 5
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=2.75480
- c5: t_us=2.72560 , e_us=3.174543961037557e-16
- c6: t_bd=10.000000 , e_bd=1.304165109239364e-14
IVP 132
Class: PINLCU
Initial conditions:
$$\begin{align}x_{0}(0)&\subset~\left[ 3.4194741518, 3.4394741518\right]\\x_{1}(0)&=-0.5571605704\\x_{2}(0)&=6.6414554255\\x_{3}(0)&=-0.4155707763\\x_{4}(0)&=11.2630437207\\x_{5}(0)&=-0.3253256691\\x_{6}(0)&=-30.1552268759\\x_{7}(0)&=-0.0240476254\\x_{8}(0)&=-21.123835338\\x_{9}(0)&=-0.1768607531\\x_{10}(0)&=3.3538695971\\x_{11}(0)&=0.5056967832\\x_{12}(0)&=5.9715695787\\x_{13}(0)&=0.3656827228\\x_{14}(0)&=14.6952576794\\x_{15}(0)&=0.1897060219\\x_{16}(0)&=1.656999664\\x_{17}(0)&=-0.2876595326\\x_{18}(0)&=28.4465098142\\x_{19}(0)&=-0.216393453\\x_{20}(0)&=1.3549401715\\x_{21}(0)&=0.2305785439\\x_{22}(0)&=2.1823149972\\x_{23}(0)&=0.1691432132\\x_{24}(0)&=6.2796052506\\x_{25}(0)&=0.0877265322\\x_{26}(0)&=1.4378575272\\x_{27}(0)&=-0.1172195431\\x_{28}(0)&=15.3882659679\\x_{29}(0)&=-0.0148647893\end{align}$$
Exact Solution*:
No exact solution provided.
View test data:
- method: HOE
- order: 10
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=0.32930
- c5: t_us=0.32300 , e_us=8.536973697056971e-08
- c6: t_bd=10.000000 , e_bd=2.869702727635592e-07
- method: HOE
- order: 15
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=0.68670
- c5: t_us=0.67240 , e_us=8.538677965554131e-08
- c6: t_bd=10.000000 , e_bd=2.874789036058645e-07
- method: HOE
- order: 20
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=1.56990
- c5: t_us=1.54950 , e_us=8.537427915317197e-08
- c6: t_bd=10.000000 , e_bd=2.881473422679248e-07
- method: HOE
- order: 5
- abs. tolerance: 1e-12
- rel. tolerance: 1e-12
- min. stepsize: 1e-05
- c4: t_c=2.79110
- c5: t_us=2.76660 , e_us=8.536211400754501e-08
- c6: t_bd=10.000000 , e_bd=2.854804710718251e-07
* rounded (non-rigorously) to 5 decimal places to preserve screen real estate.
<< back