欧拉角转换为四元数

Here is a step-by-step guide on how to convert Euler angles to quaternions using a MATLAB program, with the sequence being 312:

1. First, define the three Euler angles in radians: the rotation about the first axis (phi), the rotation about the second axis (theta), and the rotation about the third axis (psi).

2. Next, use the following equations to calculate the elements of the 3x3 rotation matrix:

```

R11 = cos(theta)*cos(psi)

R12 = sin(phi)*sin(theta)*cos(psi) - cos(phi)*sin(psi)

R13 = cos(phi)*sin(theta)*cos(psi) + sin(phi)*sin(psi)

R21 = cos(theta)*sin(psi)

R22 = sin(phi)*sin(theta)*sin(psi) + cos(phi)*cos(psi)

R23 = cos(phi)*sin(theta)*sin(psi) - sin(phi)*cos(psi)

R31 = -sin(theta)

R32 = sin(phi)*cos(theta)

R33 = cos(phi)*cos(theta)

```

3. Then, use the elements of the rotation matrix to calculate the elements of the quaternion:

```

q0 = 0.5*sqrt(R11 + R22 + R33 + 1)

q1 = (R32 - R23)/(4*q0)

q2 = (R13 - R31)/(4*q0)

q3 = (R21 - R12)/(4*q0)

```

4. Finally, output the resulting quaternion.

This MATLAB program will allow you to efficiently and accurately convert Euler angles to quaternions, which can be useful in a variety of applications, such as computer graphics and robotics.