@acer @Carl Love 

This explains many of my misinterpretations. I just realized that there is more than one Typeset command in Maple and that the typeset I use in plot commands is a structure used for type setting.

Thank you as allways!

@sursumCorda 

Yes, plot in Maple 2022 does not even need assumptions.

plot([sqrt(x*(2 - x)/3), 1 - sqrt((1 - x^2)/3)]);

Smartplot is from 1997 and may no longer be needed given the many new plot features that have been introduced since then.

interface(verboseproc = 3);
print(smartplot);

@neskopolydis 

You are are welcome. EC 2.5 is truncated to 2 (and negative values are replaced by zero).

Maybe this can help you in your explorations:

If you put EC_y to 2, MapleSim integrates two variables (the two elastic coordinates). You can see this in the console output

The corresponding equation for the bending line (for EC_y=2) for the dynamic deflection in y looks probably like this

Compare this to text book formulas for the quasi-static case

I agree that the flexible beam component deserves more explanation for better use.

@neskopolydis 

I cannot give a definition for elastic coordinates (EC), nor indicate a scientific domain where this term is commonly used.

Like me, you are guessing in the wrong direction. In my case I attributed EC to the number of coordinates of nodes (points across a structure) in finite element formulation to describe the deformation field (across an element). But that’s incorrect.

In my current interpretation I would call EC: “Coefficient of shape function”.

I had the chance to get some explanations, which allows me to say that the flexible beam component has a solid mechanical and mathematical formulation. What MapleSim achieves with the component is pretty cool: Partial differential equations are solved alongside with discrete components in a multi body environment.

Each component in MapleSim has states which describe the dynamics of the component. The states can be deduced from generalized coordinates that MapleSim determines during the simulation process. This is perhaps where the ECs got their name from. In the screen shot of the console output window below you can see how the generalized coordinates match the entries in the EC fields (u is for displacement in x, v in y and so on).

(You may want to delete the connection line to the rigid body frame and observe how the generalized coordinates change).

I would describe EC in the following way: The ECs are generalized coordinates of the flexible beam component which describe the (dynamical!) deformation of the component. The deformation is approximated with “shape” functions which are polynomials, and the EC are the coefficients of the polynomial. Such an approach is similar to the Ritz method with the difference that in a dynamic situation these coefficients have to be determined at each time step. If I am not mistaken the flexible beam component can be considered as a high fidelity finite beam element. Parameterization is like having access to a library of finite beam elements in a single component. Another cool thing.

In your load case, the shape function for EC=2 matches the shape of the deformed beam known from linear theory exactly.  A higher degree of polynomials will not give better results. As Orang said, for different load cases or constraints along the beam you might need higher polynomial orders. Alternatively, you can split the beam in two wherever a constraint or a load is applied. I have no experience which approach is better.

I hope my description is sufficiently correct. In the Multi body example “2-D Flexible Spin-up Beam” are references that I have not studied, which might give you more insight.  

@ecterrab 

"&Thanks;" for the tweak. I have noticed that in Maples doocumentation both notations dx and dx are used. The Calculus Study Guide for example uses an italic d for input in integration examples. Also wikidepdia uses different notation depending on the language when searching for "differential". From this persepective a general implementaion would make sense.

BTW: I like the term integration element that you used in "Integral Vector Calculus and parametrization of regions" to avoid calling the vektorical dr and dS in an integral a differential. This term could also be used to refer to a simple dx in an integral.

@ecterrab 

In the attached worksheet the tweak had no effect. Could you check what went wrong?

Differential_format_in_integrals_with_tweak.mw

@acer 

OK. Where can the version that created a worksheet be found?

First of all, thumbs up for this elegant way of integration and a happy new year!

I was about to see what the "inert" option does for surface integrals in your worksheet, but I can't get to this point. When I execute (with the latest official Maple version) the highlighted input below I get

The attached worksheet looses the kernel as well on my computer.

Kernel_lost.mw

Update:

I was misled by the load message. It was the physics package that was out of date

Can such a message be made more specific? I still get this message but now the kernel does not disconnect.

@Carl Love And strangely enough, it works today.

@acer 

subsop is what I was looking for.

Thank you!

@Preben Alsholm 

Thats a nice option in cases where the replaced name is not part of the integrant.

It does not work for the worksheet I have attached above (see update).

@ecterrab 

Thank you for taking the time. I will continue digging. I have just discovered the physics mini course which I think is a good template for other branches of sicence an engineering.

@ecterrab In the attached file I compared the new command with a case from classical mechanics to derive equations of motion from D'Alembert's principle. In this case I noticed a difference in sign of the output which has to be taken into account. Would it be possible to return optionally an expression

diff(diff(L,v),t)-diff(L,r)

(as in the attached) instead of an equation?

In any case LagrangeEquations makes life much easier. Great enhancement!👍👍

Lagrange_Equation.mw

@Joe Riel 

The AD/DA converters you suggested provide logic signals on the bit level. This level of detail is not required for off-the-shelf micro controllers, which I want to simulate.

The plant in my model provides real signals by using sensor components of the MapleSim library. So, in those cases I would look for  AD/DA converters that work in the signal “domain” (i.e. that discretizes a real signal).  

Looks like that there are no libraries that match my request but if there are any components that can be used in combination with MapelSim's discrete components I would be interested. AD/DA conversion is not what I am primarily looking for. I have no solution for FIR filters. A convolution component with user defined kernels would be a big step in that direction.

Thank you for indicating what is possible today.

By the way, I tried to discretize a real signal with the components you proposed but could establish a proper logic 8-bit connection with 2022.2

Update: With 2022.1 the connection works and the trigger ports a visible

@alex_b 

Thank you, that’s very helpful. I have not noticed PORT LOCATIONS and SUBSYSTEM AUTORESIZE and will have a try.