‫Welcome back.
‫And so in this video, we will derive the product of rotation matrices for our X, Y, X, so that's
‫our convention.
‫Now it's X, Y, X.
‫However, even though we've changed the convention in the fixed angle approach, we will not change
‫the order of the angles.
‫So it will still be Gummo, Betar and Alpha, just like in the previous cases and just like in the previous
‫cases, Gamma Phi, Beta Theta and then Alpha SPSSI.
‫So I could also write here Fi and then Theta and BPCI.
‫So what we are saying here now is that first rotate about the inertial x frame axis by Gamma Radians
‫or Phi Radians, then rotate about the inertia frame y axis by better radians or theta radians, and
‫then rotate about the inertia from x axis by alpha radians or BPCI radians.
‫And so this is our product of our rotation matrices.
‫You first rotate about the inertial x axis, then about the inertial y axis and then about the inertial
‫x axis again.
‫But now the angles, Gamma or PHI, they will enter into this matrix here, then the angles, beta or
‫theta, they enter into this matrix here and then the angles alpha or PSI.
‫They enter into this matrix here.
‫So you will have one R X matrix with Gamma or Phi Angles and then another R X Matrix with Alpha or PSI
‫Radians.
‫So if you write these matrices out, then you will have it like this.
‫You see two are X matrices, but you have different angles in them.
‫So again, we first multiply these matrices and then to that product we will add another matrix.
‫And so if I multiply our Y times our X, then I will get this matrix here and then I add this are X,
‫which will be this one here.
‫And then if you multiply them all together, then this is your final product of your rotation matrices.
‫And now again, this product is valid for this convention here.
‫When you rotate about fixed axis and it is also valid for our small X, small Y, small X, which is
‫when you rotate about the moving frame axis, but then the order of angles, of course, will change.
‫Now it will be Alpha, Beta and gamma.
‫So this is when you rotate about moving axis and then.
‫Well in our course it would have been BPCI here, Theta here and then Phi here.
‫So this is the procedure that is followed in order to derive all the 12 products of rotation matrices
‫for all the twenty four conventions.
‫And in the book that I had suggested you in Appendix B, you will have those products for all the conventions,
‫but now you know the procedure.
‫However, in our course we will only use this convention and of course once you choose the convention,
‫you should stick with it.
‫You should not change the conventions in one project.
‫So this will be our convention.
‫We first rotate about the moving from Z axis by BPCI Radians, then about the moving frame Y axis by
‫Theta Radians and then about the moving from x axis by five radians or alpha beta gamma in this nomenclature.
‫And so this will be the product of rotation matrices that we will use in this course.
‫Thank you very much.