Question

The 6-DOF translational equation along the \(x\)-axis is

• A. \(X=m(\dot{u}+qw-rv)\)
• B. \(X=m(\dot{v}+ru-pw)\)
• C. \(X=m(\dot{w}+pv-qu)\)
• D. \(X=I_x\dot{p}-(I_y-I_z)qr\)

Hint:

The translational equations of motion in body axes are \[ \boxed{ \begin{aligned} X&=m(\dot{u}+qw-rv), Y&=m(\dot{v}+ru-pw), Z&=m(\dot{w}+pv-qu). \end{aligned} } \] The rotational equations involve the moments \(L,\ M,\ N\).

Answer 1

The Correct Option is A

Step 1: Recall Newton's second law for aircraft translational motion. For six-degree-of-freedom (6-DOF) aircraft motion, the translational equations along the body axes are \[ \boxed{ \begin{aligned} X&=m(\dot{u}+qw-rv), Y&=m(\dot{v}+ru-pw), Z&=m(\dot{w}+pv-qu). \end{aligned} } \]

Step 2: Identify the equation along the \(x\)-axis. From the standard 6-DOF equations, \[ \boxed{ X=m(\dot{u}+qw-rv). } \] Hence, \[ \boxed{X=m(\dot{u}+qw-rv)} \] is the correct answer. Thus, \[ \boxed{(A)} \] is the correct answer.