Gyroscopic Coefficients

(12.269) |

where use has been made of Equations (12.235) and (12.236). It follows from Equations (12.262) and (12.263) that

(12.270) |

However, the second term on the right-hand side of the previous equation integrates to zero with the aid of Equation (12.261). Hence, we are left with

Let

(12.272) |

where use has been made of Equations (12.235) and (12.236). It follows from Equations (12.272) and (12.273) that

(12.273) |

However, the second term on the right-hand side of the previous equation integrates to zero with the aid of Equation (12.271). Hence, we are left with

Let

(12.275) |

where use has been made of Equations (12.248) and (12.261). It follows from Equations (12.262) and (12.263) that

(12.276) |

However, the second term on the right-hand side of the previous equation integrates to zero with the aid of Equation (12.249). Hence, we are left with

Finally, let

(12.278) |

where use has been made of Equations (12.248) and (12.271). It follows from Equations (12.272) and (12.273) that

(12.279) |

However, the second term on the right-hand side of the previous equation integrates to zero with the aid of Equation (12.249). Hence, we are left with

Incidentally, the
,
,
, and
are known collectively as *gyroscopic coefficients* (Proudman 1916).