Question Statement:
In the definition of the aircraft Euler angles @ (roll), ® (pitch), and v (yaw), the correct sequence of rotations required to make the inertial frame coincide with the aircraft body frame is
Options:
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(A) first y about z axis, second 0 about y axis, third @ about x axis
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(B) first 0 about y axis, second o about x axis, third y about z axis
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(C) first p about x axis, second 0 about y axis, third y about z axis
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(D) first y about z axis, second p about x axis, third 0 about y axis
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.31)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (1 Mark, MCQ)
- **Topic**: Strength of Materials & Elasticity (Stress and Strain Tensors & Generalized Hooke's Law)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> In the definition of the aircraft Euler angles @ (roll), ® (pitch), and v (yaw), the correct sequence of rotations required to make the inertial frame coincide with the aircraft body frame is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Strength of Materials & Elasticity** (Stress and Strain Tensors & Generalized Hooke's Law) under *Aerospace Structures*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"first y about z axis, second 0 about y axis, third @ about x axis"*: ❌ **INCORRECT**.
- **(B)** *"first 0 about y axis, second o about x axis, third y about z axis"*: ✅ **CORRECT**.
- **(C)** *"first p about x axis, second 0 about y axis, third y about z axis"*: ❌ **INCORRECT**.
- **(D)** *"first y about z axis, second p about x axis, third 0 about y axis"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.