I guess the math is right now taking revenge on my not-listening in the Rummler class. I need to solve three indefinite integrals for my thesis, but I don’t really get any further:
If anyone has a clue how to antidifferentiate them, I would be really happy to see your ideas! I only have to get rid of the large integral sign. The primitives of f(t) itself can be considered as known:
The same applies to all derivatives of f(t), so all f'(t) and f”(t) in the solution are fine.
EDIT: Christoph, a fellow student who is in Zürich right now, spent an hour on my integrals. He did not find a solution, so I guess there isn’t any. However, I tried to model my crane in a polar coordinate system, and the first results look promising. Maybe I can antidifferentiate those functions?
Have you ever noticed that MATLAB restricts variables to have a maximum length of 63 characters?
I tried to give my variables reasonable names. That means that my variable names reflect the content of the variables. Once the variables store longer terms, their names of course also get a bit lengthy. MATLAB does not seem to like this, now my code is full of warning messages:
Wikipedia says that there have been linkers which only accepted variable names with up to six characters. I don’t want to see how that source code looked like…
Just two little notes on what happened today:
Early in the morning I had an appointment with Dr. Agrawal. Actually I tried to reach him on Tuesday but he wasn’t in his office. On Wednesday I asked him if he had a couple of minutes for me, and we decided to meet on Thursday. On Thursday however, he was quite busy. Then I showed him the results which I had visualized on my Wednesdays posting and finally got my appointment for Friday. So… today we had only some shifts in the time (from “late afternoon” to 11pm, to 11am and finally to 9:45am). However, Dr. Agrawal was quite impressed of my work so far, and we discussed how to go on. This is what came out:So, after having seen this picture you know exactly what my diploma thesis will be about ;-). By the way, I decided to throw away this memo later on. Who could have imagined this?
In the evening I chatted with Susi a bit. She told me that she was fascinated by the eye wash station next to the shower I presented yesterday. I totally understand why:
This is how it looks like when the valve is reasonably wide open. Notice that the impulsion of the water from the left hand side is just the same as the impulsion from the right hand side, so the water falls down vertically in the center. (I love the term “impulsion”. Prof. Thévenin who used to teach fluid mechanics in Magdeburg used this word.)
I’m currently working on the differential flatness of cranes. Believe it or not, but all cranes I know so far are flat. If this doesn’t make sense for you, you probably don’t know what flatness is. Maybe I’ll explain it later.
EDIT: There actually are a couple of non-flat cranes. They can fly, therefore they can fly away. Then however, they just do what they want which makes them uncontrollable. And uncontrollable systems cannot be differentially flat. In Germany, people call these non-flat cranes “Kranich”.
Today, I was a bit bored all day long. Therefore I created a small simulation for two types of flat cranes: boom cranes and gantry cranes. I also added a visualization (see below). If you like these pictures (I do *g*), I still have some more.
ANOTHER EDIT: To give you just a rough idea of what differential flatness is about: It’s a property of a system that allows me to do perfect feedforward control. In this case, I selected the red trajectory of the load and could calculate the necessary blue trajectory (of the crane) in a very simple way.
Just a short one: I just looked up “Bryan Angles” on Google, also known as “Cardan Angles“.
This is what Google came up with:
Some family called “Angles” named their son “Bryan”. If they did this on purpose, he will probably have a couple of brothers called Cardan Angles, Euler Angles, Pitch Angles, Yaw Angles, …
I started to use Maple here in the institute. I really like it. It saves a lot of time and does less mistakes then I would do when calculating by hand. However, from time to time, there are really nasty things.
A couple of minutes ago, the “Execute the entire worksheet”-button was grayed out. I still was able to execute every single line, but that takes some time. I saved my worksheet and restarted Maple. Then everything was alright again. Do you know under which condition Maple disables this button?
This is how it normally looks like:
This is how it looks when Maple thinks it knows better then me:
Another thing that bothered me this morning was the “2D-Input” Mode. But I switched over to the classic redish Maple input again, so that’s fine now.
Edit: I just discovered that there are two interfaces for Maple. A good one (“Classic Worksheet Maple 10”) and a bad one (“Maple 10”). Just stick to the good one. Choose Classic Worksheet Maple. :-)