Thank you very much, various!  Hnx

@tomleslie 

Thank you very much, Tom! It's clear now - also after remark of Carl - that I goofed with the initial conditions. Although I read the error message I could not interpret it. It won't happen again! Learning every day a bit more about wonderful Maple!

@Carl Love 

Thank you very much , Carl! This is a very valuable hint. It will help me in the future because my deq's are always nasty and almost never solvable analytically.

@Preben Alsholm 

I apologize. Here it is.
 

Download Fadenpendel_exakt_2020-08-08.mw
 

Download Fadenpendel_exakt_2020-08-08.mw

@acer 

Hi acer! Yes, accuracy is not critical, approximation suffices.Thank you, acer.

To all of those who helped and hopefully also will also help me in future: You guys at MaplePrimes are really of unvaluable value!

Best regards   Heinz

@dharr 

Hi dharr!

Thank you for this hint. I looked briefly into DAE. Looks like LAGRANGE multipliers or LAGRANGE function of first kind to me. I need more time to look into it more closely. Will be back here to report. At the moment I'm abroad.

In the mean time thanks again   Heinz

@vv 

Hi vv! Thank you very much! This is super-duper! I didn't know, that diff also masters piecewise functions.

Thanks again for this vauable hint.   Heinz

@mmcdara Hi mmcdara!

Thank you very much. You saved the day!  This is exactly what I needed. Your example demonstrates neatly the structure of the MAPLE spline (I'm still a bloody beginner with MAPLE).

Thanks again   Heinz

@dharr @acer : Hi dharr, acer! Thank you very much for your answer.

My problem is as follows: Basically I was expecting an ODE-system of order 2 coming from the LAGRANGE-formalism with the general coordinates phi1(t) and phi2(t) (angles, time). The specialty is that the second independent variable phi2 doesn't appear in the ODE of second order for phi1. For phi2(t) it is just an ordinary equation with the variable phi1(t). Therefore I don't have an ODEsystem with two ODE-equations, just one ODE-equation of order 2 for phi1. This equation is highly non-linear and I have to solve it numerically. As result I get phi1(t) and I plug it into the equation for phi2. The points I get I smooth with a spline.

My problem with the derivation of splines has been solved by mmcdara, see below.

Thanks again    Heinz

@gkokovidis 

Καλημερα υ ευχαριστο πολυ! The two hints for writing if- or do-statements and procedures are very helpful.

Χαιρετισματα   Heinz

PS. That's about all I know about Greek after 5 years schooling. It's a shame.

@Preben Alsholm 

Thank you, Preben! I have done as you suggested. The next programs will be written in the new mode.
My program, phase I, works now perfectly. So I am merrily ;-) underway to phase II which will be even more complex.

Regards   Heinz

@Preben Alsholm Dear Preben, you are a great help for me, thanks! Due to your hints I have learnt a lot. I know however that I have still many, many things to learn. Sometimes really strange things happen with Maple I cannot understand.

a) An utmost simple command line is not executed. I can't find an error. If I retype the same line again it suddenly works. This leaves me puzzled.

b)Please see the attached file. These are two identical if-statements. Why does the second example work and the first one not? And why is the value of the variable h printed twice although I use a double point instead of a semicolon?

Best regards   Heinz

PS. I just noticed that the error output was not uploaded. After the first statement :Error, unterminated 'if' statement

After the second and third statement:Error, unable to parse

Download Trouble_with_if_statement_2020-06-10.mw

@Preben Alsholm Thank you, Preben. Yep, it works. But is there a possibility to extract the value of t_max when the event occurs? In this case I could use it for ODEplot and an error message could be omitted.

@Preben Alsholm Preben, thank you for your hint. I am adding an excerpt of my program. What I want to do is the following: The independet variable in the ODE is t, the depending phi1(t). The singular point is reached when phi1(t)=phi1_end. I would like the value of t=t_max at this point in order to insert it into ODEplot. If t_max is chosen only little above the corresponding value of phi1_end I get an error message from ODEplot and the plot cannot be used.
 

Download ODE_for_Preben_2020-06-09.mw

The problem is as follows: I have a differential of second order which is highly nonlinear and therefor only to solve numerically i.e. y''(t)-f(t)=0. At a certain point the equation becomes singular. I know this point in form of a constant. How can I stop dsolve, numeric at this point?