Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Glossary
_ _
V ≡ V : = V • V
The unit vector function returns the unit vector associated with a non-zero
length vector (V),
( V ) : V V
n =
The cross product between (V) and (W) which subtend an angle (ξ) results
in a bi-normal vector in the direction of the unit vector (n) defined by,
V × W : = V ⋅ W ⋅ sin ξ ⋅ nˆ
The direction of the unit vector (n) is determined by the right-hand screw
rule as (Va,b) rotates towards (W) through angle (ξ). The skew symmetric
matrix operator associated with vector (V) is,
[ V × ]
: =
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣
0
V
Z
− V
xxxix
Y
,
,
,
− V
0
V
X
Z
,
,
,
V
− V
The relationship between the vector cross product and skew symmetric
operator is then,
0.15.7 Simulation Naming Convention
[ V × ] ⋅ W ≡ V × W
C
Generic vectors ( V ) are represented by V_CAB, with components
a,
b
VX_CAB etc., and magnitude V_AB. Position vectors are typically P_CAB.
Inertial velocity, acceleration and jerk vectors are V_CAB, A_CAB, and
J_CAB, respectively. Non-inertial velocity, acceleration and jerk vectors are
DP_CAB, D2PCAB and D3PCAB respectively. Vector projections onto the
transverse, longitudinal and basic (horizontal) planes of a frame are
VR_CAB, VV_CAB and VH_CAB respectively. Angular velocity vectors
( C
ω ) are named W_CAB with components WX_CAB etc.; likewise angular
A,
B
acceleration and jerk vectors are DW_CAB and D2WCAB respectively.
0.16 Matrix Definitions
0.16.1 General Notation
Matrices are denoted by [M], their transpose by [M] T , and their inverse by
[M] -1 . If it is necessary to associate a matrix with a frame, as with the
0
Y
X
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦