【摘要】 研究相对论性非线性非完整力学系统的 Ｂｉｒｋｈｏｆｆ 表示．引入相对论性广义动能函数，采用凝固导数以及凝固偏导数，得到了相对论性非线性非完整系统凝固导数形式的 Ｄ’ Ａｌｅｍｂｅｒｔ＿ Ｌａｇｒａｎｇｅ原理、 Ｒｏｕｔｈ 方程；运动方程表成显形式，进一步实行 Ｂｉｒｋｈｏｆｆ 化，将 Ｂｉｒｋｈｏｆｆ 动力学方程推广应用于相对论性非线性非完整力学系统；并给出应用实例更多还原

【Abstract】 Birkhoff’s representation for relativistic nonlinear nonholonomic mechanical systems is studied.The relativistic generalized kinetic energy function,“freezing_derivatives”and“freezing_parlial derivatives”is introduced.The “freezing_derivatives”form D’Alembert_Lagrange principle and Routh equations for relativistic nonlinear nonholonomic dynamical systems are obtained.The equations of motion are expressed as the explicit form,then which can be expressed in form of Birkhoff.The dynamical equations of Birkhoff are generalized and applied to the relativistic nonlinear nonholonomic dynamical systems.At last an illustrative example is given.更多还原