We identify an effective proxy for the analytically unknown second integral of motion (I ₂) for rotating barred or tri-axial potentials. Planar orbits of a given energy follow a tight sequence in the space of the time-averaged angular momentum and its amplitude of fluctuation. The sequence monotonically traces the main orbital families in the Poincar map, even in the presence of resonant and chaotic orbits. This behavior allows us to define the calibrated angular momentum, the average angular momentum () normalized by the amplitude of its fluctuation (), as a numerical proxy for I ₂. It also implies that the amplitude of fluctuation in L _z , previously underappreciated, contains valuable information. This new proxy allows one to classify orbital families easily and accurately, even for real orbits in N-body simulations of barred galaxies. It is a good diagnostic tool of dynamical systems, and may facilitate the construction of equilibrium models.

我们为旋转禁止或三轴电位的运动的解析未知的二次积分 ( I ₂ )确定了一个有效的代理。给定能量的平面轨道在时间平均角动量及其波动幅度的空间中遵循紧密的序列。即使存在共振和混沌轨道，该序列也单调地追踪庞加莱映射中的主要轨道族。这种行为允许我们定义校准角动量，即由其波动幅度( ) 归一化的平均角动量( )，作为I ₂的数值代理。这也意味着L _z的波动幅度 ，以前被低估，包含有价值的信息。这种新的代理允许人们轻松准确地对轨道族进行分类，即使是对棒星系N体模拟中的真实轨道也是如此。它是一个很好的动力系统诊断工具，可以促进平衡模型的构建。