Spring 2003 16.614-1 Introduction We started with one frame(B)rotating w and accelerating w with respect to another(I), and obtained the following expression for the absolute acceleration B B 7=7m+p+2×p+d×p+d×(×p of a point located at However, in many cases there are often several intermediate frames that have to be taken into account. onsider the situation in the figure Two frames that are moving, rotating, accelerating with respect to each other and the inertial reference frame Assume that 2w and w I are given with respect to the first intermediate frame 1 o The left superscript here simply denotes a label -there are two w's to consider in this problem Note that the position of point p with respect to the origin of frame 1 is given by 7=2+3 nd the position of point P with respect to the origin of the inertial frame is given by P=17+27+37=17+ We want PlT and PlrSpring 2003 16.61 4–1 Introduction • We started with one frame (B) rotating
ω and accelerating ˙
ω with respect to another (I), and obtained the following expression for the absolute acceleration ¨
r I = ¨
r I cm + ¨ ρ
B + 2
ω × ˙ ρ
B + ˙
ω I × ρ
+
ω × (
ω × ρ
) of a point located at
r =
rcm + ρ
• However, in many cases there are often several intermediate frames that have to be taken into account. • Consider the situation in the figure: – Two frames that are moving, rotating, accelerating with respect to each other and the inertial reference frame. – Assume that 2
ω and 2 ˙
ω 1 are given with respect to the first intermediate frame 1. ✸ The left superscript here simply denotes a label – there are two
ω’s to consider in this problem. • Note that the position of point P with respect to the origin of frame 1 is given by P1
r = 2
r + 3
r and the position of point P with respect to the origin of the inertial frame is given by P I
r = 1
r + 2
r + 3
r ≡ 1
r + P1
r • We want P I ˙
r I and P I¨
r I