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where the last term is zero, since ''A'' is conserved in a collision.
where the last term is zero, since ''A'' is conserved in a collision.
因为 <math>g</math> 在碰撞中守恒，所以最后一项为零。
因为 <math>A</math> 在碰撞中守恒，所以最后一项为零。
Letting <math>A = m</math>, the mass of the particle, the integrated Boltzmann equation becomes the conservation of mass equation:<ref name="dG1984" />{{rp|pp 12,168}}
Letting <math>A = m</math>, the mass of the particle, the integrated Boltzmann equation becomes the conservation of mass equation:<ref name="dG1984" />{{rp|pp 12,168}}
令 <math>A=m</math>，即粒子质量，积分后的玻尔兹曼方程化为质量守恒方程<ref name="dG1984" />{{rp|pp 12,168}}：
令 <math>A=m</math>，即粒子质量，积分后的玻尔兹曼方程化为质量守恒方程<ref name="dG1984" />{{rp|pp 12,168}}：
where <math>\rho = mn</math> is the mass density, and <math>V_i = \langle w_i\rangle</math> is the average fluid velocity.
where <math>\rho = mn</math> is the mass density, and <math>V_i = \langle w_i\rangle</math> is the average fluid velocity.
<math>\rho=mn</math> 为质量密度，<math>V_i=\langle w_i\rangle</math> 为平均流体速度。
Letting <math>A = p_i</math>, the momentum of the particle, the integrated Boltzmann equation becomes the conservation of momentum equation:<ref name="dG1984" />{{rp|pp 15,169}}
Letting <math>A = p_i</math>, the momentum of the particle, the integrated Boltzmann equation becomes the conservation of momentum equation:<ref name="dG1984" />{{rp|pp 15,169}}
令 <math>A = p_i</math>，即粒子动量，积分后的玻尔兹曼方程化为动量守恒方程<ref name="dG1984" />{{rp|pp 15,169}}：
:<math>\frac{\partial}{\partial t}(\rho V_i) + \frac{\partial}{\partial x_j}(\rho V_i V_j+P_{ij}) - nF_i = 0,</math>
:<math>\frac{\partial}{\partial t}(\rho V_i) + \frac{\partial}{\partial x_j}(\rho V_i V_j+P_{ij}) - nF_i = 0,</math>
where <math>P_{ij} = \rho \langle (w_i-V_i) (w_j-V_j) \rangle</math> is the pressure tensor (the [[wikipedia:Viscous_stress_tensor|viscous stress tensor]] plus the hydrostatic [[wikipedia:Pressure|pressure]]).
where <math>P_{ij} = \rho \langle (w_i-V_i) (w_j-V_j) \rangle</math> is the pressure tensor (the [[wikipedia:Viscous_stress_tensor|viscous stress tensor]] plus the hydrostatic [[wikipedia:Pressure|pressure]]).
<math>P_{ij}=\rho\langle (w_i-V_i) (w_j-V_j) \rangle</math> 为压强张量（{{le|粘性应力张量|viscous stress tensor}}加上流体静力学[[压强]]）。
Letting <math>A =\frac{p_i p_i}{2m}</math>, the kinetic energy of the particle, the integrated Boltzmann equation becomes the conservation of energy equation:<ref name="dG1984" />{{rp|pp 19,169}}
Letting <math>A =\frac{p_i p_i}{2m}</math>, the kinetic energy of the particle, the integrated Boltzmann equation becomes the conservation of energy equation:<ref name="dG1984" />{{rp|pp 19,169}}
令 <math>A =\frac{p_i p_i}{2m}</math>，即粒子动能，积分后的玻尔兹曼方程化为能量守恒方程<ref name="dG1984" />{{rp|pp 19,169}}：
:<math>\frac{\partial}{\partial t}(u + \tfrac{1}{2}\rho V_i V_i) + \frac{\partial}{\partial x_j} (uV_j + \tfrac{1}{2}\rho V_i V_i V_j + J_{qj} + P_{ij}V_i) - nF_iV_i = 0,</math>
:<math>\frac{\partial}{\partial t}(u + \tfrac{1}{2}\rho V_i V_i) + \frac{\partial}{\partial x_j} (uV_j + \tfrac{1}{2}\rho V_i V_i V_j + J_{qj} + P_{ij}V_i) - nF_iV_i = 0,</math>
where <math>u = \tfrac{1}{2} \rho \langle (w_i-V_i) (w_i-V_i) \rangle</math> is the kinetic thermal energy density, and <math>J_{qi} = \tfrac{1}{2} \rho \langle(w_i - V_i)(w_k - V_k)(w_k - V_k)\rangle</math> is the heat flux vector.
where <math>u = \tfrac{1}{2} \rho \langle (w_i-V_i) (w_i-V_i) \rangle</math> is the kinetic thermal energy density, and <math>J_{qi} = \tfrac{1}{2} \rho \langle(w_i - V_i)(w_k - V_k)(w_k - V_k)\rangle</math> is the heat flux vector.
<math>u=\tfrac{1}{2}\rho\langle (w_i-V_i) (w_i-V_i) \rangle</math> 为动力热能密度（kinetic thermal energy density），<math>J_{qi}=\tfrac{1}{2}\rho\langle (w_i-V_i)(w_k-V_k)(w_k-V_k)\rangle</math> 热通量矢量。
===Hamiltonian mechanics 哈密顿力学===
===Hamiltonian mechanics 哈密顿力学===