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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; JSFH JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A satellite orbiting about earth. LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= At a specific time, LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= QyQvSTcjbXN1YihtaSgidCIpLG1uKCIwIikpRzYiIiIhISIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder , its location and velocity vectors in a Cartesian coordinate set ( LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= QyQtSS9TZXRDb29yZGluYXRlc0c2IjYjLkkqY2FydGVzaWFuR0YlISIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= ) are known in Km and Km/s respectively: LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= QyY+SSNyMEc2Ii1JJDwsPkdGJTYlIiU3Ty1JIi1HNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYtSShfc3lzbGliR0YlNiMiJVY6IiV0ZCIiIj5JNyNtc3ViKG1pKCJ2IiksbW4oIjAiKSlHRiUtRic2JSQiJSNRIyEiJC1GKzYjJCIlO3VGPS1GKzYjJCIlNj9GPUY2 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNyMEdGKC1JJ1JUQUJMRUdGKDYlIilPRCFlKS1JJ01BVFJJWEdGKDYjNyU3IyIlN083IyElVjo3IyIldGQmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRjw2Iy9JJCVpZEdGKEYx LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+STcjbXN1YihtaSgidiIpLG1uKCIwIikpR0YoLUknUlRBQkxFR0YoNiUiKT9IIWUpLUknTUFUUklYR0YoNiM3JTcjJCIlI1EjISIkNyMkISU7dUY5NyMkISU2P0Y5JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZANiMvSSQlaWRHRihGMQ== Note the change to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjcjBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn. It's not a good idea to assign to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+, then to use LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as a variable. The object LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+ is actually a table entry to a table now named LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, so use of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= as the radius function later on just causes all kinds of grief. You can get around this by setting LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+ as a "Atomic Identifier," namely, as a single symbol not connected to a table name. This can only be done as a GUI operation either through the format menu or through the Context Menu. However, you might already have done that for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+, so I don't know why it wouldn't have been done for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+. I had trouble with the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+ until I renamed it. ??? LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= At a time QyQ+STcjbXN1YihtaSgidCIpLG1uKCIxIikpRzYiLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRilJKF9zeXNsaWJHRiU2JCQiI0QhIiIiJStPRjI=[s] the satellite propultion system inject it with a velocity pulse PkkpJkRlbHRhO3ZHNiItSSQ8LD5HRiQ2JSQiI0shIiItSSItRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEkvVmVjdG9yQ2FsY3VsdXNHNiRGLkkoX3N5c2xpYkdGJDYjJCIiJkYqLUYsNiMkIiM3Rio= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSkmRGVsdGE7dkdGKC1JJ1JUQUJMRUdGKDYlIilLPGcpKi1JJ01BVFJJWEdGKDYjNyU3IyQiI0shIiI3IyQhIiZGOTcjJCEjN0Y5JkknVmVjdG9yR0YlNiNJJ2NvbHVtbkdGKDcjLUZANiMvSSQlaWRHRihGMQ== Calculate the satelite orbit from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPS9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRj4= to QyQvSTcjbXN1YihtaSgidCIpLG1pKCJFIikpRzYiLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRilJKF9zeXNsaWJHRiU2JCIiJiIlK08hIiI= [s]. LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder JSFH JSFH Defining the satellite location verctor QyQ+SSJyRzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkPCw+R0YlNiUtSSJ4R0YlNiM5JC1JInlHRiVGMS1JInpHRiVGMUYlRiVGJSEiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder the differential equation of the satellite motion is LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= PiZJJG9kZUc2IjYjSSJWR0YlLUkiK0c2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRitJKF9zeXNsaWJHRiU2JC1JJWRpZmZHRis2JS1JInJHRiU2I0kidEdGJUY4RjgtSSIqR0YqNiQtRjo2JEkjbXVHRiVGNSokLUklTm9ybUdGJTYjRjUhIiQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+Jkkkb2RlR0YoNiNJIlZHRigtSSdSVEFCTEVHRig2JSIpJzQwZSktSSdNQVRSSVhHRig2IzclNyMsJi1JJWRpZmZHRiY2JC1JInhHRig2I0kidEdGKC1JIiRHRiY2JEZBIiIjIiIiKigsKCokRj5GRUZGKiQtSSJ5R0YoRkBGRUZGKiQtSSJ6R0YoRkBGRUZGIyEiJEZFSSNtdUdGKEZGRj5GRkZGNyMsJi1GPDYkRktGQkZGKihGSEZQRlJGRkZLRkZGRjcjLCYtRjw2JEZORkJGRiooRkhGUEZSRkZGTkZGRkYmSSdWZWN0b3JHRiU2I0knY29sdW1uR0YoNyMtRmduNiMvSSQlaWRHRihGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= (The problem with what you had was that you equated a vector to a scalar zero. At that point, I think you're dead in the water. After dropping the scalar zero, you could convert the vector to a list or set with the convert command. That would allow you to insert the result into the dsolve command. My choice of equating each component to zero isn't strictly necessary.)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= PkkicUc2IjwjJi1JJ0VxdWF0ZUdGJDYkJkkkb2RlR0YkNiNJIlZHRiQtSSQ8LD5HRiQ2JSIiIUYxRjFGJA== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJxR0YoPCUvLCYtSSVkaWZmR0YmNiQtSSJ4R0YoNiNJInRHRigtSSIkR0YmNiRGNyIiIyIiIiooLCgqJEY0RjtGPCokLUkieUdGKEY2RjtGPCokLUkiekdGKEY2RjtGPCMhIiRGO0kjbXVHRihGPEY0RjxGPCIiIS8sJi1GMjYkRkFGOEY8KihGPkZGRkhGPEZBRjxGPEZJLywmLUYyNiRGREY4RjwqKEY+RkZGSEY8RkRGPEY8Rkk3IzwlLywmLUYyNiQtRjI2JEY0RjdGN0Y8Rj1GPEZJLywmLUYyNiQtRjI2JEZBRjdGN0Y8Rk5GPEZJLywmLUYyNiQtRjI2JEZERjdGN0Y8RlNGPEZJ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH NiI= JSFH I ran this search for an analytic solution for about 15 minutes. I don't think Maple is going to find one, and if it does, it's going to be a very messy expression. I think I'll go with a numeric solution. That's going to require given LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy a numeric value,and also imposing the initial conditions. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= QyU+SSdpbml0czFHNiImLUknRXF1YXRlR0koX3N5c2xpYkdGJTYkLUkickdGJTYjIiIhSSNyMEdGJUYlIiIiPkknaW5pdHMyR0YlJi1GKDYkLUkkPCw+R0YlNiUtLUkiREc2JCUqcHJvdGVjdGVkR0YpNiNJInhHRiVGLS0tRjs2I0kieUdGJUYtLS1GOzYjSSJ6R0YlRi1JNyNtc3ViKG1pKCJ2IiksbW4oIjAiKSlHRiVGJQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdpbml0czFHRig2JS8tSSJ4R0YoNiMiIiEiJTdPLy1JInlHRihGMiElVjovLUkiekdGKEYyIiV0ZDclRi9GNUY5 LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdpbml0czJHRig2JS8tLUkiREdGJTYjSSJ4R0YoNiMiIiEkIiUjUSMhIiQvLS1GMjYjSSJ5R0YoRjUkISU7dUY5Ly0tRjI2I0kiekdGKEY1JCElNj9GOTclRi9GOkZB 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At this point, I called the numeric ODE developer who informed me that these questions had already reached his desk, and he gave answers to the last 3. A definitive answer to the first question is in the hands of the analytic ODE developer, and that's why Support is waiting to get back to you. The question about the velocity boost has a simple answer in Maple. One uses the "events" property of dsolve/numeric. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= When I was led to the answer about events, I noticed that the formal response from the developer included answers to the last three questions. You will eventually get this response from Support, so don't tell them that you already got it from me. _____________________________________________________________ I (the developer) can only comment on the numeric questions 2-4: 2) The only way to integrate this equation is as 3 separate odes, so decomposing into 3 equations and 6 ICs. This is not a dreadfully difficult task, and can be accomplished in 1 line: odes := convert(lhs(ode[V][1]), set); 3) We don't directly handle integration of the Matrix form. In any event, in this case it would be less efficient, as Matrix form requires first order, so we'd need to convert first, then the Matrix would be quite sparse, as only one equation would contain each of the second derivatives. It's far more effficient to handle this as a system. 4) The velocity pulse can easily be handled using dsolve/numeric's event features (see ?dsolve,events). Here's a simpler example using a single ODE: > dsys := {diff(x(t),t,t)=0, x(0)=0, D(x)(0)=1}: > evt := [t=1, diff(x(t),t)=diff(x(t),t)-2]: > dsn := dsolve(dsys, numeric, events=[evt]); dsn := proc(x_rkf45) ... end proc > plots[odeplot](dsn,0..2); 1+ AAA + AAA AAA + AA AA + AA AA 0.8+ AAA AAA + AAA AAA + AAA AAA + AA AA 0.6+ AA AA + AAA AAA + AAA AAA + AA AA 0.4+ AAA AAA + AAA AAA + AAA AAA + AA AA 0.2+ AA AA + AAA AAA + AAA AAA +AAA AAA -**--+--+---+---+--+---+--+---+--+---+---+--+---+--+---+--+---+--+---+--**- 0.5 1 1.5 2 So this example had an initial velocity of 1, and a velocity pulse of -2 was introduceed at t=1 making the velocity -2 for the rest of the integration. ________________________________________________________________________ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Guys, How do I let Maple try to solve this set of equations symbolically? Is there an efficient way to integrate this set of equations numerically? - That is not to start and decompose it into 3 equations and 6 ICs... How can you convert the system into a Matrix form and integrate it ? How can I "inject" the extra propultion pulse to the solution? Is solving for t = 2.5 hours and them placing new ICs and solving again is the only way?
<Text-field style="Heading 1" layout="Heading 1">Seperating the Set of Equations</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder Error, invalid input: lhs received Vector(3, {(1) = diff(diff(x(t), t), t)+mu*x(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (2) = diff(diff(y(t), t), t)+mu*y(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (3) = diff(diff(z(t), t), t)+mu*z(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2)}, attributes = [coords = cartesian]), which is not valid for its 1st argument, expr Error, invalid input: lhs received Vector(3, {(1) = diff(diff(x(t), t), t)+mu*x(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (2) = diff(diff(y(t), t), t)+mu*y(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (3) = diff(diff(z(t), t), t)+mu*z(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2)}, attributes = [coords = cartesian]), which is not valid for its 1st argument, expr Error, invalid input: lhs received Vector(3, {(1) = diff(diff(x(t), t), t)+mu*x(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (2) = diff(diff(y(t), t), t)+mu*y(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2), (3) = diff(diff(z(t), t), t)+mu*z(t)/(x(t)^2+y(t)^2+z(t)^2)^(3/2)}, attributes = [coords = cartesian]), which is not valid for its 1st argument, expr JSFH %; JSFH JSFH
JSFH JSFH JSFH TTdSMApJNVJUQUJMRV9TQVZFLzg1ODAyNTM2WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQiJTdPISVWOiIldGRGJQ==TTdSMApJNVJUQUJMRV9TQVZFLzg1ODAyOTIwWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQkIiUjUSMhIiQkISU7dUYrJCElNj9GK0YlTTdSMApJNVJUQUJMRV9TQVZFLzk4NjAxNzMyWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQkIiNLISIiJCEiJkYrJCEjN0YrRiU=TTdSMApJNVJUQUJMRV9TQVZFLzg1ODA1MDk2WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJi0lJWRpZmZHNiQtRis2JC0lInhHNiMlInRHRjJGMiIiIiooLCgqJEYvIiIjRjMqJC0lInlHRjFGN0YzKiQtJSJ6R0YxRjdGMyMhIiRGNyUjbXVHRjNGL0YzRjMsJi1GKzYkLUYrNiRGOUYyRjJGMyooRjVGPkZARjNGOUYzRjMsJi1GKzYkLUYrNiRGPEYyRjJGMyooRjVGPkZARjNGPEYzRjNGJQ==