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Spring 2003 16.614-3 And acceleration Pl I P1:I PI I dt 1 t r+ +1×+1×F . Now substitute and condense Pr“I I F+2( P1)+ 1 1×P+× I r+ {2+(2+2×号2)+2×+2x +2(d×12+3 22×°T {27+37}+5×(×{27+57} +272+32+2(+2×3号2)+2(1d “T+ 2×(2×37)+1×(×[+37)+21×(2×37Spring 2003 16.61 4–3 And acceleration: P I¨ r I = 1¨ r I + P1¨ r I ≡ P Ia = 1¨ r I + dI dt P1 ˙ r I = 1¨ r I + dI dt P1 ˙ r 1 + (1 ω × P1 r ) = 1¨ r I + P1¨ r 1 + 1 ω × P1 ˙ r 1 + 1 ˙ ω I × P1 r +1 ω × P1 ˙ r 1 + 1 ω × P1 r • Now substitute and condense. P I¨ r I = 1¨ r I + P1¨ r 1 + 2(1 ω × P1 ˙ r 1 ) + 1 ˙ ω I × P1 r + 1 ω × ( 1 ω × P1 r ) = 1¨ r I + 2¨ r 1 + (3¨ r 2 + 2(2 ω × 3 ˙ r 2 ) + 2 ˙ ω 1 × 3 r + 2 ω × ( 2 ω × 3 r )) +2 1 ω × 2 ˙ r 1 + 3 ˙ r 2 + 2 ω × 3 r +1 ˙ ω I × 2 r + 3 r + 1 ω × ( 1 ω × 2 r + 3 r ) = 1¨ r I + 2¨ r 1 + 3¨ r 2 + 2([1 ω + 2 ω] × 3 ˙ r 2 ) + 2(1 ω × 2 ˙ r 1 ) +1 ˙ ω I × 2 r + [1 ˙ ω I + 2 ˙ ω 1 ] × 3 r +2 ω × ( 2 ω × 3 r ) + 1 ω × ( 1 ω × [ 2 r + 3 r ]) + 21 ω × ( 2 ω × 3 r )