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3.1.2 Rotational Motion about CG The derivation starts with the Euler’s 2nd axiom: m g i d dt I g b/i i d dt I g b/n b d dt I g b/n b/n I g b/n I g b/n I g b/n b/n # Rotational Motion about CG Expressed in {b} b I g b/n SI g b b b/n b/n m g b where I g is the inertia matrix where I x , I y , and I z are the moments of inertia about {b} and I xy =I yx , I xz =I zx and I yz =I zy are the products of inertia defined as: I g : I x I xy I xz I yx I y I yz , I g I g 0 # I zx I zy I z I x V y 2 z 2 m dV; I y V x 2 z 2 m dV; I z V x 2 y 2 m dV; I xy V xy m dV V yx m dV I yx I xz V xz m dV V zx m dV I zx I yz V yz m dV V zy m dV I zy 6 Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)
3.1.3 Equations of Motion about CG The Newton-Euler equations can be represented in matrix form according to: CG M RB b v g/n b b/n CG C RB b v g/n b b/n f g b m g b # Expanding the matrices give: Isaac Newton (1642-1726) Leonhard Euler (1707-1783) mI 33 0 33 b v g/n b b/n mS b b/n 0 33 0 33 SI g b b/n b v g/n b b/n f g b m g b # 0 33 I g CG M RB CG C RB 7 Lecture Notes TTK 4190 Guidance and Control of Vehicles (T. I. Fossen)
Page 1 and 2: Chapter 3 - Rigid-Body Kinetics 3.1
Page 3 and 4: 3.1 Newton-Euler Equations of Motio
Page 5: 3.1.1 Translational Motion about CG
Page 9 and 10: 3.2 Newton-Euler Equations of Motio
Page 11 and 12: 3.2.1 Translational Motion about CO
Page 13 and 14: 3.3 Rigid-Body Equations of Motion
Page 15 and 16: 3.3.1 Nonlinear 6-DOF Rigid-Body Eq
Page 17 and 18: 3.3.1 Nonlinear 6-DOF Rigid-Body Eq
Page 19 and 20: 3.3.2 Linearized 6-DOF Rigid-Body E
Page 21: 3.3.2 Linearized 6-DOF Rigid-Body E

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