This paper aims to explore the development of a flight dynamics model for a small-scale side-by-side helicopter and describe its trim and stability characteristics. The helicopter is considered a suitable candidate for Urban Air Mobility (UAM) solutions, because of its reliable design and low noise characteristics, but still very small knowledge is present on the mathematical modeling approaches and dynamic properties. A 14 degrees of freedom nonlinear mathematical model is developed and semi-analytical models are employed to account for the presence of the shrouds. An iterative trim routine is developed and applied with a suitable control mix that allows the use of classic helicopter controls. To control the vertical speed and roll rate, the paper assumes an equal collective pitch and lateral cyclic in the two rotors, while a uniform plus a differential longitudinal cyclic is adopted for pitch and yaw maneuvers. The paper discusses unique characteristics of the side-by-side configuration as obtained from the stability analysis: an unstable high-frequency mode, governed by the vertical velocity and pitch angle arises when the center of gravity (CG) of the vehicle is aligned or placed in front of the two main rotors. Similarly, both lateral phugoid and roll subsidence modes are sensitive to the CG location. The side-by-side configuration presents also a stable spiral mode which needs to be carefully designed.

中文翻译：

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城市空中交通小型并排直升机的飞行动力学建模和稳定性

本文旨在探索小型并列直升机飞行动力学模型的开发，并描述其配平和稳定性特性。由于其可靠的设计和低噪声特性，直升机被认为是城市空中交通（UAM）解决方案的合适候选者，但对数学建模方法和动态特性的了解仍然很少。开发了 14 个自由度的非线性数学模型，并采用半解析模型来解释护罩的存在。开发了迭代配平例程，并与合适的控制组合一起应用，允许使用经典的直升机控制。为了控制垂直速度和滚转速率，本文假设两个旋翼的集体螺距和横向循环相等，而俯仰和偏航机动采用均匀加微分纵向循环。本文讨论了从稳定性分析中获得的并排配置的独特特征：当车辆的重心 (CG) 对齐或对齐时，会出现由垂直速度和俯仰角控制的不稳定高频模式。放置在两个主旋翼的前面。类似地，横向沉降模式和滚动沉降模式都对重心位置敏感。并排配置还呈现出需要仔细设计的稳定螺旋模式。