i discovered a weird behavior using ```NDSolve``` to solve a set of differential equations.
Let me outline my problem:
I need to solve a set of differential equations. These are equations of motion where the number of equations is depending on the number of shape functions i use.
If i use 8 shape functions i'll get a set of 8 differential equations which NDSolve is evaluating. So there are 8 generalized coordinates (from Subscript[qq, 1][t] to Subscript[qq, 8][t]) which need to be solved via NDSolve.
If i switch the number of shape functions to 9 which means i'll get 9 equations to solve, the NDSolve function is reporting the error message NDSolve::ntdvdae: Cannot solve to find an explicit formula for the derivatives. NDSolve will try solving the system as differential-algebraic equations.
(Please find the list of 8 and the list of 9 equations below to copy paste it into Mathematica. Furthermore i added the syntax i used for solving these equations. See also the initial conditions below in the code.)
(I use Version 12.1.1.0)
Since i need to solve it for 9 (or more) shape functions/equations i wanted to ask you guys if anybody can please help me fixing my problem? I looked it up on the internet but have no idea on how to fix it and i really appreciate any hint of you guys ;-)
Here's the list with 8 equations to solve
ListDGL8={-129.006137732798*Sin[334.7356174047985*t] + 16038.147354412993*Subscript[qq, 1][t] + 8019.073677207725*Subscript[qq, 2][t] + 6961.710838517229*Subscript[qq, 3][t] + 6433.029419170023*Subscript[qq, 4][t] + 6085.362833097541*Subscript[qq, 5][t] + 5828.203660787876*Subscript[qq, 6][t] + 5627.085115515234*Subscript[qq, 7][t] + 5464.773786742095*Subscript[qq, 8][t] + 0.12299999999999997*Derivative[2][Subscript[qq, 1]][t] + 0.06149999999999988*Derivative[2][Subscript[qq, 2]][t] + 0.035142857142857226*Derivative[2][Subscript[qq, 3]][t] + 0.021964285714285738*Derivative[2][Subscript[qq, 4]][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 5]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 6]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 7]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 8]][t] == 0, -64.50306886639892*Sin[334.7356174047985*t] + 8019.073677206336*Subscript[qq, 1][t] + 12830.008260286922*Subscript[qq, 2][t] + 12301.32684094079*Subscript[qq, 3][t] + 11550.385255502828*Subscript[qq, 4][t] + 10889.951086133398*Subscript[qq, 5][t] + 10344.260387403454*Subscript[qq, 6][t] + 9896.079764234863*Subscript[qq, 7][t] + 9525.500273098965*Subscript[qq, 8][t] + 0.0615*Derivative[2][Subscript[qq, 1]][t] + 0.03514285714285714*Derivative[2][Subscript[qq, 2]][t] + 0.021964285714285714*Derivative[2][Subscript[qq, 3]][t] + 0.014642857142857124*Derivative[2][Subscript[qq, 4]][t] + 0.010250000000000037*Derivative[2][Subscript[qq, 5]][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 6]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 7]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 8]][t] == 0, -36.656551732634455*Sin[334.7356174047985*t] + 6961.710838516545*Subscript[qq, 1][t] + 12301.326840942595*Subscript[qq, 2][t] + 14022.914961281625*Subscript[qq, 3][t] + 14397.108145685284*Subscript[qq, 4][t] + 14318.736070694373*Subscript[qq, 5][t] + 14083.571128609241*Subscript[qq, 6][t] + 13802.756401830295*Subscript[qq, 7][t] + 13520.571185562003*Subscript[qq, 8][t] + 0.03514285714285714*Derivative[2][Subscript[qq, 1]][t] + 0.021964285714285714*Derivative[2][Subscript[qq, 2]][t] + 0.014642857142857124*Derivative[2][Subscript[qq, 3]][t] + 0.010250000000000037*Derivative[2][Subscript[qq, 4]][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 5]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 6]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 7]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 8]][t] == 0, -22.733293165752244*Sin[334.7356174047985*t] + 6433.029419171642*Subscript[qq, 1][t] + 11550.385255508896*Subscript[qq, 2][t] + 14397.108145690378*Subscript[qq, 3][t] + 15694.295645717299*Subscript[qq, 4][t] + 16267.381548618549*Subscript[qq, 5][t] + 16480.82839766756*Subscript[qq, 6][t] + 16509.967514004966*Subscript[qq, 7][t] + 16444.178366731503*Subscript[qq, 8][t] + 0.021964285714285714*Derivative[2][Subscript[qq, 1]][t] + 0.014642857142857124*Derivative[2][Subscript[qq, 2]][t] + 0.010250000000000037*Derivative[2][Subscript[qq, 3]][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 4]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 5]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 6]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 7]][t] + 0.0027032967032967203*Derivative[2][Subscript[qq, 8]][t] == 0, -15.02696945487861*Sin[334.7356174047985*t] + 6085.362831948756*Subscript[qq, 1][t] + 10889.951086136134*Subscript[qq, 2][t] + 14318.736070694926*Subscript[qq, 3][t] + 16267.381548612495*Subscript[qq, 4][t] + 17397.880350381078*Subscript[qq, 5][t] + 18054.639540893724*Subscript[qq, 6][t] + 18428.607549193897*Subscript[qq, 7][t] + 18629.97845286259*Subscript[qq, 8][t] + 0.014642857142857124*Derivative[2][Subscript[qq, 1]][t] + 0.010250000000000037*Derivative[2][Subscript[qq, 2]][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 3]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 4]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 5]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 6]][t] + 0.0027032967032967203*Derivative[2][Subscript[qq, 7]][t] + 0.0021964285714285714*Derivative[2][Subscript[qq, 8]][t] == 0, -10.429113172009295*Sin[334.7356174047985*t] + 5828.203660786874*Subscript[qq, 1][t] + 10344.26038740584*Subscript[qq, 2][t] + 14083.571128609183*Subscript[qq, 3][t] + 16480.82839766034*Subscript[qq, 4][t] + 18054.639540892793*Subscript[qq, 5][t] + 19102.808844437823*Subscript[qq, 6][t] + 19807.616279822425*Subscript[qq, 7][t] + 20283.79973727325*Subscript[qq, 8][t] + 0.010250000000000037*Derivative[2][Subscript[qq, 1]][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 2]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 3]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 4]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 5]][t] + 0.0027032967032967203*Derivative[2][Subscript[qq, 6]][t] + 0.0021964285714285714*Derivative[2][Subscript[qq, 7]][t] + 0.0018088235294117516*Derivative[2][Subscript[qq, 8]][t] == 0, -7.5222261315258265*Sin[334.7356174047985*t] + 5627.085115509573*Subscript[qq, 1][t] + 9896.079764229798*Subscript[qq, 2][t] + 13802.756401820458*Subscript[qq, 3][t] + 16509.96751398605*Subscript[qq, 4][t] + 18428.60754918051*Subscript[qq, 5][t] + 19807.616279809037*Subscript[qq, 6][t] + 20810.86977714626*Subscript[qq, 7][t] + 21548.654009568505*Subscript[qq, 8][t] + 0.007454545454545436*Derivative[2][Subscript[qq, 1]][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 2]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 3]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 4]][t] + 0.0027032967032967203*Derivative[2][Subscript[qq, 5]][t] + 0.0021964285714285714*Derivative[2][Subscript[qq, 6]][t] + 0.0018088235294117516*Derivative[2][Subscript[qq, 7]][t] + 0.0015073529411764874*Derivative[2][Subscript[qq, 8]][t] == 0, -5.597559240622573*Sin[334.7356174047985*t] + 5464.773801028572*Subscript[qq, 1][t] + 9525.500273096026*Subscript[qq, 2][t] + 13520.571185554669*Subscript[qq, 3][t] + 16444.178366715205*Subscript[qq, 4][t] + 18629.97845285246*Subscript[qq, 5][t] + 20283.799737262772*Subscript[qq, 6][t] + 21548.65400957316*Subscript[qq, 7][t] + 22526.08801129856*Subscript[qq, 8][t] + 0.005590909090909091*Derivative[2][Subscript[qq, 1]][t] + 0.004300699300699318*Derivative[2][Subscript[qq, 2]][t] + 0.003379120879120845*Derivative[2][Subscript[qq, 3]][t] + 0.0027032967032967203*Derivative[2][Subscript[qq, 4]][t] + 0.0021964285714285714*Derivative[2][Subscript[qq, 5]][t] + 0.0018088235294117516*Derivative[2][Subscript[qq, 6]][t] + 0.0015073529411764874*Derivative[2][Subscript[qq, 7]][t] + 0.0012693498452012453*Derivative[2][Subscript[qq, 8]][t] == 0}; Here's the list with 9 equations to solve
ListDGL9={-129.006137732798*Sin[334.73556652336856*t] + 16038.147354411205*Subscript[qq, 1][t] + 8019.073677208609*Subscript[qq, 2][t] + 6961.710838517458*Subscript[qq, 3][t] + 6433.029418026366*Subscript[qq, 4][t] + 6085.362832099767*Subscript[qq, 5][t] + 5828.2036607934715*Subscript[qq, 6][t] + 5627.085123744895*Subscript[qq, 7][t] + 5464.773809254926*Subscript[qq, 8][t] + 5331.03754389986*Subscript[qq, 9][t] + 0.12299999999999997*Derivative[2][Subscript[qq, 1]][t] + 0.06149999999999988*Derivative[2][Subscript[qq, 2]][t] + 0.035142857142857226*Derivative[2][Subscript[qq, 3]][t] + 0.021964285714285738*Derivative[2][Subscript[qq, 4]][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 5]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 6]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 7]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 8]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 9]][t] == 0, -64.50306886639892*Sin[334.73556652336856*t] + 8019.0736772033815*Subscript[qq, 1][t] + 12830.008260288385*Subscript[qq, 2][t] + 12301.326840941168*Subscript[qq, 3][t] + 11550.385255510206*Subscript[qq, 4][t] + 10889.95108613008*Subscript[qq, 5][t] + 10344.26038741265*Subscript[qq, 6][t] + 9896.079764221562*Subscript[qq, 7][t] + 9525.500273072714*Subscript[qq, 8][t] + 9216.11355334177*Subscript[qq, 9][t] + 0.06149999999999988*Derivative[2][Subscript[qq, 1]][t] + 0.035142857142857226*Derivative[2][Subscript[qq, 2]][t] + 0.021964285714285738*Derivative[2][Subscript[qq, 3]][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 4]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 5]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 6]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 7]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 8]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 9]][t] == 0, -36.656551732634455*Sin[334.73556652336856*t] + 6961.710838512762*Subscript[qq, 1][t] + 12301.326840944486*Subscript[qq, 2][t] + 14022.914961282135*Subscript[qq, 3][t] + 14397.108145694714*Subscript[qq, 4][t] + 14318.736070690153*Subscript[qq, 5][t] + 14083.571128621115*Subscript[qq, 6][t] + 13802.75640181324*Subscript[qq, 7][t] + 13520.5711855283*Subscript[qq, 8][t] + 13254.50707224186*Subscript[qq, 9][t] + 0.035142857142857226*Derivative[2][Subscript[qq, 1]][t] + 0.021964285714285738*Derivative[2][Subscript[qq, 2]][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 3]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 4]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 5]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 6]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 7]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 8]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 9]][t] == 0, -22.733293165752244*Sin[334.73556652336856*t] + 6433.029419167233*Subscript[qq, 1][t] + 11550.385255511093*Subscript[qq, 2][t] + 14397.10814569096*Subscript[qq, 3][t] + 15694.29564572827*Subscript[qq, 4][t] + 16267.381548613543*Subscript[qq, 5][t] + 16480.828397681238*Subscript[qq, 6][t] + 16509.967513985117*Subscript[qq, 7][t] + 16444.178366692387*Subscript[qq, 8][t] + 16330.908579364535*Subscript[qq, 9][t] + 0.021964285714285738*Derivative[2][Subscript[qq, 1]][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 2]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 3]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 4]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 5]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 6]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 7]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 8]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 9]][t] == 0, -15.02696945487861*Sin[334.73556652336856*t] + 6085.3628319438685*Subscript[qq, 1][t] + 10889.951086138535*Subscript[qq, 2][t] + 14318.736070695479*Subscript[qq, 3][t] + 16267.381548624719*Subscript[qq, 4][t] + 17397.880350375548*Subscript[qq, 5][t] + 18054.639540908975*Subscript[qq, 6][t] + 18428.60754917178*Subscript[qq, 7][t] + 18629.9784528194*Subscript[qq, 8][t] + 18724.397981297923*Subscript[qq, 9][t] + 0.014642857142857091*Derivative[2][Subscript[qq, 1]][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 2]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 3]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 4]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 5]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 6]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 7]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 8]][t] + 0.0018088235294117583*Derivative[2][Subscript[qq, 9]][t] == 0, -10.429113172009295*Sin[334.73556652336856*t] + 5828.20366078161*Subscript[qq, 1][t] + 10344.260387408489*Subscript[qq, 2][t] + 14083.571128609881*Subscript[qq, 3][t] + 16480.82839767344*Subscript[qq, 4][t] + 18054.63954088709*Subscript[qq, 5][t] + 19102.808844453888*Subscript[qq, 6][t] + 19807.616279798793*Subscript[qq, 7][t] + 20283.79973722587*Subscript[qq, 8][t] + 20605.19607634237*Subscript[qq, 9][t] + 0.010250000000000066*Derivative[2][Subscript[qq, 1]][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 2]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 3]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 4]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 5]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 6]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 7]][t] + 0.0018088235294117583*Derivative[2][Subscript[qq, 8]][t] + 0.001507352941176465*Derivative[2][Subscript[qq, 9]][t] == 0, -7.5222261315258265*Sin[334.73556652336856*t] + 5627.085115504011*Subscript[qq, 1][t] + 9896.079764232622*Subscript[qq, 2][t] + 13802.756401821214*Subscript[qq, 3][t] + 16509.96751399996*Subscript[qq, 4][t] + 18428.607549174223*Subscript[qq, 5][t] + 19807.61627982615*Subscript[qq, 6][t] + 20810.869777121115*Subscript[qq, 7][t] + 21548.65400951868*Subscript[qq, 8][t] + 22096.273533439962*Subscript[qq, 9][t] + 0.0074545454545454*Derivative[2][Subscript[qq, 1]][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 2]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 3]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 4]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 5]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 6]][t] + 0.0018088235294117583*Derivative[2][Subscript[qq, 7]][t] + 0.001507352941176465*Derivative[2][Subscript[qq, 8]][t] + 0.0012693498452012474*Derivative[2][Subscript[qq, 9]][t] == 0, -5.597559240622573*Sin[334.73556652336856*t] + 5464.773801022766*Subscript[qq, 1][t] + 9525.500273098907*Subscript[qq, 2][t] + 13520.571185555425*Subscript[qq, 3][t] + 16444.178366729408*Subscript[qq, 4][t] + 18629.978452845942*Subscript[qq, 5][t] + 20283.79973728105*Subscript[qq, 6][t] + 21548.65400954662*Subscript[qq, 7][t] + 22526.08801124734*Subscript[qq, 8][t] + 23288.863232276402*Subscript[qq, 9][t] + 0.005590909090909075*Derivative[2][Subscript[qq, 1]][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 2]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 3]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 4]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 5]][t] + 0.0018088235294117583*Derivative[2][Subscript[qq, 6]][t] + 0.001507352941176465*Derivative[2][Subscript[qq, 7]][t] + 0.0012693498452012474*Derivative[2][Subscript[qq, 8]][t] + 0.001078947368421073*Derivative[2][Subscript[qq, 9]][t] == 0, -4.2742528997234785*Sin[334.73556652336856*t] + 5331.037487920821*Subscript[qq, 1][t] + 9216.113553331204*Subscript[qq, 2][t] + 13254.507072221313*Subscript[qq, 3][t] + 16330.908579346724*Subscript[qq, 4][t] + 18724.397981263348*Subscript[qq, 5][t] + 20605.19607633236*Subscript[qq, 6][t] + 22096.273533398286*Subscript[qq, 7][t] + 23288.863232202362*Subscript[qq, 8][t] + 24251.03528175503*Subscript[qq, 9][t] + 0.00430069930069936*Derivative[2][Subscript[qq, 1]][t] + 0.003379120879120816*Derivative[2][Subscript[qq, 2]][t] + 0.002703296703296745*Derivative[2][Subscript[qq, 3]][t] + 0.0021964285714285636*Derivative[2][Subscript[qq, 4]][t] + 0.0018088235294117583*Derivative[2][Subscript[qq, 5]][t] + 0.001507352941176465*Derivative[2][Subscript[qq, 6]][t] + 0.0012693498452012474*Derivative[2][Subscript[qq, 7]][t] + 0.001078947368421073*Derivative[2][Subscript[qq, 8]][t] + 0.0009248120300751469*Derivative[2][Subscript[qq, 9]][t] == 0}; This works perfectly
NDSolve[{ListDGL8, Table[Subscript[qq, i][0] == 0, {i, 1, 8, 1}],Table[Subscript[qq, i]'[0] == 0, {i, 1, 8, 1}]},Table[Subscript[qq, i][t], {i, 1, 8, 1}], {t, 0, 0.2}, MaxSteps -> \[Infinity]] But this doesn't work
NDSolve[{ListDGL9, Table[Subscript[qq, i][0] == 0, {i, 1, 9, 1}],Table[Subscript[qq, i]'[0] == 0, {i, 1, 9, 1}]}, Table[Subscript[qq, i][t], {i, 1, 9, 1}], {t, 0, 0.2}, MaxSteps -> \[Infinity]]