A ship with controls fixed is modeled as a two degrees of freedom system. For the linear maneuvering equations of motion for coupled sway and yaw, if the derived eigenvalues are real and negative, then the ship must possess:
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- Positional motion stability
- Directional stability
- Straight line stability
- Both directional and positional motion stabilities
The Correct Option is C
Solution and Explanation
Step 1: Understand the significance of eigenvalues.
In a two degrees of freedom system for coupled sway and yaw, the eigenvalues of the system matrix determine the stability of the ship's motion: - Real and negative eigenvalues imply that any deviation from equilibrium decays over time, resulting in a stable response.
Step 2: Relate eigenvalues to straight-line stability.
Straight-line stability refers to the ship's ability to maintain a straight trajectory or return to a straight course after being disturbed. In this context: - Negative eigenvalues indicate the damping effect in both sway and yaw motions, ensuring that the ship naturally returns to a straight-line motion over time.
Step 3: Analyze other options.
Positional motion stability (Option A): This refers to the ship's ability to maintain its position, which is not directly determined by sway and yaw dynamics.
Directional stability (Option B): While it involves yaw stability, it does not fully describe the straight-line motion stability as required in this question.
Both directional and positional motion stabilities (Option D): This is broader than what the eigenvalues of sway and yaw specifically describe.
Conclusion: If the eigenvalues of the coupled sway and yaw system are real and negative, the ship possesses straight-line stability.
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