Sum of two vectors

edit

The problem is that diff(a_V_ra,t) is giving you a column vector and vector([0,0,-g]) is giving you a row vector. Further, Sage sees the first as a matrix and the second as a vector. You can fix this using .column() as you did earlier in your code.

a_a_ra = diff(a_V_ra,t)+vector([0,0,-g]).column()

gives:

[ cos(psi)*D[0](v)(t)]
[-sin(psi)*D[0](v)(t)]
[                  -g]

My full code is:

var('psi t g')
v = function('v',t)

R_ra=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

r_V_ra = vector([v,0,0])
a_V_ra = R_ra*r_V_ra.column()
a_a_ra = diff(a_V_ra,t)+vector([0,0,-g]).column()

Maybe you can try something like that:

sage: m=matrix([[1],[0],[0]])
sage: v=vector([0,5,6])
sage: m.column(0)+v
(1, 5, 6)