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Theron Hitchman
College Mathematics Teaching, only mostly insane.
College Mathematics Teaching, only mostly insane.

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Triple Pendulum Control

A few years ago Dr. Tobias Glück from Technische Universität Wien, found that along with his mathematical insights, computers and numerical methods were now fast enough to swing-up and balance a pendulum, on a pendulum, on pendulum on a sliding rail under computer control.

IEEE CSS Video Clip Contest 2014 Submission

Triple Pendulum on a Cart (YT ~1 min.):

The presented work deals with the swing-up of the triple pendulum on a cart. The swing-up maneuver is accomplished within a two-degrees-of-freedom control scheme consisting of a nonlinear feedforward controller and an optimal feedback controller. Based on a precise mathematical model, the feedforward controller was obtained by solving a nonlinear two-point boundary value problem with free parameters. A time-variant Riccati Controller was developed in order to stabilize the system along the nominal trajectory and an Extended Kalman Filter was used to estimate the non-measurable states. The overall control strategy for the swing-up maneuver was successfully implemented and tested on an experimental test bench. Up to the authors’ knowledge, this is the first contribution so far providing numerical and experimental results of the swing-up maneuver for a triple pendulum on a cart.

Paper (open pdf):

Tobias Glück:

Here is an easy to follow and graphic explanation of Kalman filters due to Tim Babb, who lives in the San Francisco Bay Area, and is Lighting Optimization Lead for Pixar Animation Studios.

Related Post:

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That is very nice.
This is very cool. It relies on:

- elementary results about symmetric polynomials
- polynomials over C have finitely many roots
- elementary results about sequences
- continuity of polynomials
- the implicit function theorem (for polynomials!)
- a non-empty closed and open subspace of a connected space is the whole space

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This site has been posting biographies of prominent Latin and Hispanic mathematicians once a day for National Hispanic Heritage Month, with nine remaining to be revealed. I'm bookmarking it as a useful source for potential expansions to Wikipedia — fewer of these people have articles than I think probably should.

(As for why "Latin and Hispanic" is not redundant: see

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This is thing. I am pretty excited about it.

I just need to find enough students to make it run.

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So... I wonder what others think.

I am open to this. I have been teaching linear algebra for a few years, now, and maybe I agree with this.

What say you?

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All the major professional societies say so!
CBMS Statement on Active Learning
Okay, this is a really big deal.  The Conference Board of the Mathematical Sciences has weighed in. CBMS supports active learning ( CBMS Active Learning Statement )! Just to be clear, this isn't one or two professors clicking a like button on social media. ...

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James Maynard has been counting prime numbers that don't have the number 7 as a digit. As he informed us at the recent European Congress of Mathematics, he has proved that there are infinitely many of them.

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That's adorable.
Harry's face says it all. Mandrake Baby Photoshoot by Jesse and Katherine Oldfield:

Hope +Scott Peters​​ is having fun at the USWNT game.

Drink water and stay cool!

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New +Shapeways Inc​ stuff today. The purple one is a Steinmetz surface. The bronze one is the trefoil as a (2,3) torus knot.

I think it's (2,3). It might be (3,2). I forget which way to put the parameters. Anyway, this if the one where the order two symmetry is more obvious.

More is supposed to arrive tomorrow.
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