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Unformatted text preview: force balance equations can be expressed in the compact and convenient form f load,x load,y At + f = 0,
(1) (p ) (1) (p ) f load,x = (f1 , . . . , f1 ) ∈ Rp , f load,y = (f2 , . . . , f2 ) ∈ Rp ,
(p+1) f anch = (f1 (n ) (p+1) , . . . , f1 , f2 (n ) , . . . , f2 ) ∈ R2(n−p) , and A ∈ R2n×m is a matrix that can be found from the geometry data (truss topology and
node positions). You may refer to A in your solutions to parts (a) and (b). For part (c), we
have very kindly provided the matrix A for you in the m-ﬁle, to save you the time and trouble
of working out the force balance equations from the geometry of the problem.
14.7 Quickest take-oﬀ. This problem concerns the braking and thrust proﬁles for an airplane during
take-oﬀ. For simplicity we will use a discrete-time model. The position (down the runway) and the
velocity in time period t are pt and vt , respectively, for t = 0, 1, . . .. These satisfy p0 = 0, v0 = 0,
and pt+1 = pt + hvt , t = 0, 1, . . ., where h > 0 is the sampling time period. The velocity updates as
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid