Tham khảo tài liệu 'crc press mechatronics handbook 2002 by laxxuss episode 3 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Using Stokes s theorem one has T i dA X V r B - B V X r dA j i dA X B or T iA X B m X B The electromagnetic torque T acts on the infinitesimal current loop in a direction to align the magnetic moment m with the external field B and if m and B are misaligned by the angle Ỡ we have T mB sin e The incremental potential energy and work are found as dW dn T de mBsine de and W n -mBcose -m B Using the electromagnetic force we have dW -dn F dr -Vn dr and F -Vn V m B m V B Coordinate Systems and Electromagnetic Field The transformation from the inertial coordinates to the permanent-magnet coordinates is cos ey cos ez cos ey sin ez - sin ey x r Tr r sin ex sin ey cos ez - cos ex sin ez sin ex sin ey sin ez cos ex sin ez sin ex cos ey y cos ex sin ey cos ez sin ex sin ez cos ex sin ey sin ez - sin ex cos ez cos ex cos ey z x x r y r y z z We use the transformation matrix cos ey cos ez Tr sin ex sin ey cos ez - cos ex sin ez cos ex sin ey cos ez sin ex sin ez cos ey sin ez - sin ey sin ex sin ey sin ez cos ex sin ez sin ex cos ey cos ex sin ey sin ez - sin ex cos ez cos ex cos ey If the deflections are small we have 1 ez -ey T rs ez 1 ex ey -ex 1 2002 CRC Press LLC Using Stokes s theorem one has T i dA X V r B - B V X r dA j i dA X B or T iA X B m X B The electromagnetic torque T acts on the infinitesimal current loop in a direction to align the magnetic moment m with the external field B and if m and B are misaligned by the angle Ỡ we have T mB sin e The incremental potential energy and work are found as dW dn T de mBsine de and W n -mBcose -m B Using the electromagnetic force we have dW -dn F dr -Vn dr and F -Vn V m B m V B Coordinate Systems and Electromagnetic Field The transformation from the inertial coordinates to the permanent-magnet coordinates is cos ey cos ez cos ey sin ez - sin ey x r Tr r sin ex sin ey cos ez - cos ex sin ez sin ex sin ey sin ez cos ex sin ez sin ex cos ey y cos ex sin ey cos ez sin ex sin ez cos ex sin ey sin ez - sin ex cos ez cos ex cos ey z x
