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% Rolling coin problem in Section 8-8
% This is also a good review of rolling contact.
%
% Set up problem
overwrite on
newtonian n
frames a,b,c
bodies d % so that D will have inertia
% Mass center of D is point do
constants r,g,i
mass d=m
j=m*r^2/4
i_d_do>>=j*d1>*d1>+2*j*d2>*d2>+j*d3>*d3>
points dhat
variables h'',l'',s'',f{3}
%
% Rotation matrices
simprot(n,a,2,i)
simprot(a,b,3,h)
simprot(b,c,-1,L)
simprot(c,d,2,s)
%
% Rotational kinematics
% Note that we don't need to form w_a_n>=0>
% explicitly, since a can serve as our Newtonian
% reference frame just as well as N can.
w_b_a>=h'*b3>
w_c_b>=-l'*c1>
w_d_c>=s'*d2>
w_d_a>=w_b_a>+w_c_b>+w_d_c>
alf_d_a>=dt(w_d_a>,d) % Million dollar formula under the covers
% Could also do dt(w_d_a>,a)
% Question: Why do we want to calculate alf_d_a>?
%
% Translational kinematics
v_dhat_a>=0> % Rolling contact
p_dhat_do>=r*c3>
express(w_d_a>,c)
v_do_a>=v_dhat_a>+cross(w_d_a>,p_dhat_do>)
a_do_a>=dt(v_do_a>,a) % Million dollar formula again
% Question: Could I say a_dhat_a>=0> and then used two points