## Assn 10

Now there is a forum for this.

### Re: Assn 10

Questions about gamma:

In the r-p formulation, the gamma is 7*nb. This is gamma hat right? Does this mean the gamma for the Euler normalization constraint is included in this?

In the r-w formulation, the gamma (not hat) is 6*nb. This means the Euler constraint is not included in this, right?

Thanks,

Anne

In the r-p formulation, the gamma is 7*nb. This is gamma hat right? Does this mean the gamma for the Euler normalization constraint is included in this?

In the r-w formulation, the gamma (not hat) is 6*nb. This means the Euler constraint is not included in this, right?

Thanks,

Anne

### Re: Assn 10

Gamma hat is what you get when you consider one of the GCons, take two time derivatives, and move everything to the right hand side. The gamma for the Euler Parameter Normalization constraint is called gamma superscript p and it's in the notes, somewhere.

when you add all the gamma hat from GCons and all the gamma p from Eul Par. Norm. Constr. you should get something that is 7nb.

i hope this helps.

dan

when you add all the gamma hat from GCons and all the gamma p from Eul Par. Norm. Constr. you should get something that is 7nb.

i hope this helps.

dan

### Re: Assn 10

this is pretty much what I was thinking. Just needed confirmation.

### Re: Assn 10

On the syllabus, it says prove eq.14 of Anitescu-tasora paper for HW10. Do we need to do that? I guess that the answer is no? I would be curious however to see this paper.

### Re: Assn 10

ME751Anne wrote:On the syllabus, it says prove eq.14 of Anitescu-tasora paper for HW10. Do we need to do that? I guess that the answer is no? I would be curious however to see this paper.

as i said many times, you are a person ahead of your time. we are five lectures away from that. you'll see that, and it's not pretty.

dan

### Re: Assn 10

Problem 4: What do you mean 2 plots for x and 2 plots for y? Or do you mean 2 plots, 1 for x and 1 for y?

### Re: Assn 10

i meant one plot for x, one plot for y.

dn

dn

### Re: Assn 10

From slide 29 of 3/11, the acceleration terms are calculated along with the LaGrange terms. However, in the Inverse Dynamic slides, the steps say to calculate the accelerations first, then find the LaGrange multiplier terms. Why isn't step 1 and step 2 of performing inverse dynamics combined? Is the method on slide 29 of 3/11 just a more succinct way of calculating the unknowns?

### Re: Assn 10

for problem 4, are we just supposed to get horizontal lines with the a and B values given to us?

### Re: Assn 10

ME751Chris wrote:From slide 29 of 3/11, the acceleration terms are calculated along with the LaGrange terms. However, in the Inverse Dynamic slides, the steps say to calculate the accelerations first, then find the LaGrange multiplier terms. Why isn't step 1 and step 2 of performing inverse dynamics combined? Is the method on slide 29 of 3/11 just a more succinct way of calculating the unknowns?

Chris - since the number of unknowns in Inverse Dynamics is equal to the number of constraints you can solve for the acceleration using the acceleration kinematic constraint equation. This is a linear system of dimension 7nb X 7nb. Then you can solve for the Lagrange Multipliers using the Newton-Euler EOMs. This is another linear system of dimension 7nb X 7nb.

Indeed, you can combine the two steps and solve in one shot a linear system of dimension 14nb X 14nb. If you don't have a sparse solver and use the dense linear solver from MATLAB, for instance, the second approach is four times more time consuming (since the number of operations scales like the cube of the number of equations in a linear system and the second approach has twice the number of equations compared to the first one: 2^3=8; yet in the first case you solve two 'cheaper' linear systems: 8/2=4 times more expensive).

If this doesn't make sense we can talk after class today.

dan

### Re: Assn 10

ME751Chris wrote:for problem 4, are we just supposed to get horizontal lines with the a and B values given to us?

The part that says 'Experiment with other α and β values as well to gauge the sensitivity of the solution of these two parameters' is meant to ask you to start changing these two values to see how the response of the system changes. Do this if you are curious, no need to plot anything or turn in anything beyond just plotting the response for the \alpha=0 and \beta=1 . Given that you have the MATLAB code it's easy to run it six or seven times to understand how the system response changes when \alpha and \beta change.

### Re: Assn 10

I think the y(t) given in number 5 is incorrect. It doesn't agree with the IVP. Also, when I make my convergence plot, I get that my error increases as my step size decreases. Since I used the same approach as in the handout (using Newton-Raphson with an implicit integrator), I am more inclined to believe that the y(t) given is incorrect. As a smaller step size is used, the solution is more accurate and will thus diverge farther from this 'inaccurate' y(t) given.

### Re: Assn 10

ME751Anne wrote:I think the y(t) given in number 5 is incorrect. It doesn't agree with the IVP. Also, when I make my convergence plot, I get that my error increases as my step size decreases. Since I used the same approach as in the handout (using Newton-Raphson with an implicit integrator), I am more inclined to believe that the y(t) given is incorrect. As a smaller step size is used, the solution is more accurate and will thus diverge farther from this 'inaccurate' y(t) given.

I was able to prove that the y(t) was correct using Maple.

### Re: Assn 10

Did you make the convergence plot?

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