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Helicopter Flight Dynamics Chapter 3:  Helicopter Motion Equations
General Statement Origin   For rigid body motion   :  velocity of mass center :  angular velocity of rigid body : angular momentum ,[object Object],[object Object],[object Object]
Helicopter Motion Equations Origin   For rigid body motion   :  velocity of mass center :  angular velocity of rigid body : angular momentum ,[object Object],[object Object],[object Object]
Helicopter Motion Equations Longitudinal Motion   is the summation of aerodynamic forces along the  x  axis. The three items in the right side are equivalent to  ma . The first item comes from the acceleration, while the last two items are the inertial accelerations produced by the helicopter curve motions.
Helicopter Motion Equations For the pitching motion, we have: The lift side  is the summation of aerodynamic moments . In the right side , the first item is the inertial moment caused by angular acceleration, the second item is the gyro moment, and the third item is effect of centripetal force. Lateral/yaw Motion
Helicopter Motion Equations The Relationship Between Angular Motions The attitude angles are respect to gravity axes. While the angular velocities  are measured in body axes. The 6 equations of helicopter body and 3 angular motion equations consists of the governing equations of helicopter flight dynamics.  The relationship between angular velocities and  helicopter attitudes rates can be written as: Z D Z 1 Y 1 X 1
Summation ,[object Object],[object Object],[object Object],[object Object],Stability Analysis Control Analysis
Helicopter Motion Equations Linearization of Helicopter Flight Dynamic Equations Motivations ,[object Object],[object Object],[object Object],Feasibility For the start time of external perturbation, the variation of motion is small with respect to the reference steady state condition (trim condition) and can be treated as linear variation approximately.
Helicopter Motion Equations Assumptions: ,[object Object],3.  Neglecting the items of more than second order  ,[object Object],[object Object],2)  The variations of forces are small so that:
Helicopter Motion Equations Longitudinal Motion Equations in Hover Lateral/yaw Motion Equations in Hover ,[object Object],[object Object],[object Object]

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直升机飞行力学 Helicopter dynamics chapter 5

  • 1. Helicopter Flight Dynamics Chapter 3: Helicopter Motion Equations
  • 2.
  • 3.
  • 4. Helicopter Motion Equations Longitudinal Motion is the summation of aerodynamic forces along the x axis. The three items in the right side are equivalent to ma . The first item comes from the acceleration, while the last two items are the inertial accelerations produced by the helicopter curve motions.
  • 5. Helicopter Motion Equations For the pitching motion, we have: The lift side is the summation of aerodynamic moments . In the right side , the first item is the inertial moment caused by angular acceleration, the second item is the gyro moment, and the third item is effect of centripetal force. Lateral/yaw Motion
  • 6. Helicopter Motion Equations The Relationship Between Angular Motions The attitude angles are respect to gravity axes. While the angular velocities are measured in body axes. The 6 equations of helicopter body and 3 angular motion equations consists of the governing equations of helicopter flight dynamics. The relationship between angular velocities and helicopter attitudes rates can be written as: Z D Z 1 Y 1 X 1
  • 7.
  • 8.
  • 9.
  • 10.