Christopher2222

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10 years, 344 days

MaplePrimes Activity


These are answers submitted by Christopher2222

Yes, if you use back quotes around your primed variable.

`A'`:=t

                     

You can select cells and merge using options with the left click section by section. 

Here is a roadmap - a template if you will

`#mscripts(mi("H"),none(),none(),none(),none(),mn("3"),mn("9"))`[7]^2

                                                                              


              

 

Easier, you could do ...

assume(x>0)

simplify(combine(f,trig))


If you mean the yellow line isn't touching the green line, it's because your viewing area you set for each plot doesn't allow the values for the green line to reach the yellow line, or vice versa.

You've combined the graphs fine with display.  If you think they should intercept, then you need to solve the two equations in the yellow and green pots for x and use that as one of your extents in the range of your plots.

Alternatively as a for loop, (albeit using the list way is not efficient)

a:=[]:
for i in A2 do
  for j in A1 do
    a:=[op(a),j/i]:
  end do:
end do:
print(a)

                     

Starting with the position vector

r2:=<x1(t)|y1(t)|z1(t)> #your r2 position row vector as a function of time.
T:=Matrix(3,3,[[T1,T2,T3],[T4,T5,T6],[T7,T8,T9]]) #your transormation matrix
r1:=r2.T #your r1 position vector
Since the transformation matrix isn't itself a function of time in our example
d(r1)/dt is just d(r2)/dt .T    since d(T)/dt is zero.  and then the acceleration is simply d(d(r1)/dt)/dt

Does this answer the first part of your question?

 

 

Sorry to bring this old post up (a search led me to this post).  However this actually was possible back in 2006.  In 2006 that would be Maple 10 at the time.  Kitonums solution here https://www.mapleprimes.com/questions/200601-Labels-Above-Axis#answer202152
actually works without the align command option. 

I removed a lot of the outputs in the file, they seemed to filled with hyperlink errors or something.  Anyway don't know if it helps but you can load the sheet into Maple now.

triangle_analysis2.mw

The operator may have mistyped something.  I have given him a free pass and typed it out.  Not responsible for any errors I may have made, but I have fixed it and reuploaded it 3 times already for various errors (I'm done with that).


 

restart

with(Physics)

Setup(mathematicalnotation = true)

Eq1 := m1*l1^2*(diff(theta1(t), t, t))+(1/2)*m2*(2*l1^2*(diff(theta1(t), t, t))+2*l1*l2*(diff(theta2(t), t, t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t)))+2*l1*l2*(diff(theta2(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(theta2(t)))) = thaw1-thaw2

m1*l1^2*(diff(diff(theta1(t), t), t))+(1/2)*m2*(2*l1^2*(diff(diff(theta1(t), t), t))+2*l1*l2*(diff(diff(theta2(t), t), t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t)))+2*l1*l2*(diff(theta2(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(theta2(t)))) = thaw1-thaw2

(1)

Eq2 := (1/2)*m2*(2*l2^2*(diff(theta2(t), t, t))+2*l1*l2*(diff(theta1(t), t, t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(t)))) = thaw2

(1/2)*m2*(2*l2^2*(diff(diff(theta2(t), t), t))+2*l1*l2*(diff(diff(theta1(t), t), t))*(sin(theta1(t))*sin(theta2(t))+cos(theta1(t))*cos(theta2(t))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1(t))*sin(theta2(t))+sin(theta1(t))*(diff(theta2(t), t))*cos(theta2(t))-(diff(theta1(t), t))*sin(theta1(t))*cos(theta2(t))-cos(theta1(t))*(diff(theta2(t), t))*sin(t)))) = thaw2

(2)

``

(1/2)*m2*(2*l2^2*(diff(diff(theta2(t), t), t))+2*l1*l2*(diff(diff(theta1(t), t), t))*(sin(theta1)*sin(theta2)+cos(theta1)*cos(theta2))+2*l1*l2*(diff(theta1(t), t))*((diff(theta1(t), t))*cos(theta1)*sin(theta2)+sin(theta1)*(diff(theta2(t), t))*cos(theta2)-(diff(theta1(t), t))*sin(theta1)*cos(theta2)-cos(theta1)*(diff(theta2(t), t))*sin(theta2)))

(3)

solve([Eq1, Eq2], {diff(theta1(t), t, t), diff(theta2(t), t, t)})

{diff(diff(theta1(t), t), t) = (-sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2+sin(theta1(t))*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2+sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2-sin(theta2(t))*cos(theta1(t))*(diff(theta2(t), t))^2*l1*l2^2*m2+sin(theta1(t))*sin(theta2(t))*l1*thaw2+cos(theta1(t))*cos(theta2(t))*l1*thaw2-thaw1*l2+thaw2*l2)/(l1^2*(-2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2+sin(theta1(t))^2*sin(theta2(t))^2*m2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*m2+cos(theta1(t))^2*cos(theta2(t))^2*m2-m1-m2)*l2), diff(diff(theta2(t), t), t) = (4*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2-6*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))^3*l1^2*l2^3*m2^2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*sin(t)*l1^2*l2^3*m2^2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))^3*sin(t)*l1^2*l2^3*m2^2+2*sin(theta2(t))*cos(theta1(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*sin(t)*l1^2*l2^3*m2^2-2*sin(theta2(t))*cos(theta1(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))^3*sin(t)*l1^2*l2^3*m2^2+sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2-sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2+sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2-sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2^2+2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2*thaw1-2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2^2*m2*thaw2-2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2^2*m2*thaw1+2*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2^2*m2*thaw2+sin(theta1(t))*sin(theta2(t))*l2*m2*thaw1-sin(theta1(t))*sin(theta2(t))*l2*m2*thaw2+cos(theta1(t))*cos(theta2(t))*l2*m2*thaw1-cos(theta1(t))*cos(theta2(t))*l2*m2*thaw2-l1*m1*thaw2-l1*m2*thaw2-2*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2+4*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2-2*sin(theta1(t))^2*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))^3*l1^2*l2^3*m2^2-2*sin(theta2(t))^2*cos(theta1(t))^2*(diff(theta1(t), t))^3*(diff(theta2(t), t))*l1^2*l2^3*m2^2+2*sin(theta2(t))^2*cos(theta1(t))^2*(diff(theta1(t), t))^2*(diff(theta2(t), t))^2*l1^2*l2^3*m2^2-sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2+sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2-sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta2(t), t))^2*l1*l2^2*m2^2+sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta2(t), t))^2*l1*l2^2*m2^2-2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw1+2*sin(theta1(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw2+2*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw1-2*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2^2*m2*thaw2)/(l1*l2^2*(-2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))^2*sin(theta2(t))*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta1(t))*sin(theta2(t))^2*cos(theta1(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2-2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))^2*l1*l2*m2+2*sin(theta1(t))*cos(theta1(t))*cos(theta2(t))^2*(diff(theta1(t), t))*(diff(theta2(t), t))*l1*l2*m2+2*sin(theta2(t))*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))^2*l1*l2*m2-2*cos(theta1(t))^2*cos(theta2(t))*(diff(theta1(t), t))*(diff(theta2(t), t))*sin(t)*l1*l2*m2+sin(theta1(t))^2*sin(theta2(t))^2*m2+2*sin(theta1(t))*sin(theta2(t))*cos(theta1(t))*cos(theta2(t))*m2+cos(theta1(t))^2*cos(theta2(t))^2*m2-m1-m2)*m2)}

(4)

````


 

Download freepass2.mw

Use the with(Physics) package to take a derivative of a derivative.

with(Physics):

It appears they used mathematica to build the olympic Velodrom http://www.wolfram.com/customer-stories/key-features-of-mathematica-used-for-the-olympic-velodrome.html

They mention Fresnel integrals, and then it looks like they used an interpolation function (I think that function does what we succeded in doing with Maple back in 2011 - Can we get an exact curve fitting line) to get very good estimates of values without consuming large amounts of calculation time.  Looking further into it I find Track transition curve  which mentions a Euler sprial for the "easement" curve. 

Sorry, that's all I have for you now. 

See the writeto command.  That might be what you're looking for.

Wait, the derivative wrt a derivative?  I think the Physics package diff will do what you want it to do.

with(Physics):

Your dL/d(dq1) will be diff(L,diff(q1(t),t))

and then simply what you had in your original " d (dL/d(dq1)) dt  "  will then just be diff(diff(L,diff(q1(t),t)),t)

I think that is what you are asking.

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