理论力学Theoretical mechanics

理论力学总结，包括静力学三要素、主要研究的问题、公理、约束、平面力系、空间力系，运动学的定义，动量定理、动量矩定理等内容。

理论力学 Theoretical mechanics

• 静力学 statics
  • 研究物体在力的作用下平衡规律 Study the law of balance of objects under the action of force
  • 三要素 Three elements
    • 大小 Magnitude
    • 方向 direction
    • 作用点 Point of application
  • 主要研究的问题 Main research question
    • 物体的受力分析 Force analysis of objects
    • 力系的等效替换（或简化） Equivalent replacement (or simplified) of force system
    • 建立力系的平衡条件 Establish the balance condition of the force system
  • 公理 axiom
    • 力的平行四边形法则 The parallelogram law of force
    • 二力平衡条件为等大，反向，共线 The two-force balance condition is equal, reverse and collinear
    • 在任一原有力系上加上或减去任意的平衡力系，与原力系对刚体的作用效果等效 Adding or subtracting any balance force system to or from any original force system is equivalent to the effect of the original force system on rigid bodies
    • 作用力和反作用力总是同时存在，两力大小相等，方向相反，沿着同一条直线，分别作用在两个相互作用的物体上 The acting force and the reaction force always exist at the same time, the two forces are equal in magnitude, opposite in direction, and act on the two interacting objects along the same straight line.
    • 变形体在某一力系作用下处于平衡，如将此变形体刚化为刚体，其平衡状态保持不变 The deformed body is in equilibrium under the action of a certain force system. If the deformed body is rigidized into a rigid body, its equilibrium state remains unchanged
  • 约束 Binding
    • 位移受到限制的物体（非自由体），对其位移起到限制作用的周围物体称为约束 Objects whose displacement is restricted (non-free bodies), and the surrounding objects that restrict their displacement are called binding
  • 平面力系 Plane force system
    • 平面汇交力系 Plane Convergence Force System
    • 平面力矩、力偶 Plane moment, force couple
    • 力的平移 Force translation
  • 空间力系 Space Force System
    • 空间汇交力系
    • 空间力矩、力偶
    • 力的平移
  • 摩擦 friction
    • 摩擦角 Friction angle
    • 自锁现象 Self-locking phenomenon
      • 作用在物体上的全部主动力的合力Fr的作用线在摩擦角之内，且指向支承面，则无论这个力多大，物体必保持静止 The line of action of the resultant force Fr of all the main forces acting on the object is within the friction angle and points to the supporting surface. No matter how great the force is, the object must remain stationary
        • 如千斤顶、压榨机、圆锥销 Such as jacks, presses, taper pins
• 运动学 Kinematics
  • 研究物体运动的几何性质 Study the geometric properties of object motion
  • 点 point
    • 矢量法 Vector method
      • 以矢量表示的点的运动方程 The equation of motion of a point expressed as a vector
    • 直角坐标法 Cartesian coordinates
      • 以直角坐标表示点的运动方程 The equation of motion of a point expressed in rectangular coordinates
    • 自然法
    • 合成运动 Synthetic movement
      • 绝对运动 Absolute movement
        • 动点对于定参考系的运动 The movement of a moving point with respect to a fixed reference frame
      • 相对运动 Relative motion
        • 动点对于动参考系的运动 The movement of the moving point with respect to the moving reference frame
      • 牵连运动 Implicated movement
        • 动参考系相对于定参考系的运动 The motion of the dynamic reference frame relative to the fixed reference frame
  • 刚体 rigid body
    • 简单运动 Simple exercise
      • 平移 Panning
      • 定轴转动 Fixed axis rotation
        • 角速度 Angular velocity
        • 转角 Corner
        • 速度 speed
        • 加速度 Acceleration
    • 平面运动 Plane motion
      • 基点法 Base point method
      • 瞬心法 Instant Center Method
• 动力学 dynamics
  • 研究物体的机械运动与作用力之间的关系 Study the relationship between the mechanical motion of an object and the force
  • 动量定理 Momentum theorem
    • 定义： 动量：质量与速度的乘积 Momentum: Product of mass and speed 冲量：作用力与作用时间的乘积 Impulse: the product of force and time
    • 质点动量的增量等于作用在质点上的力的元冲量 The increase in momentum of the particle is equal to the elemental impulse of the force acting on the particle
  • 动量矩定理 Theorem of moment of momentum
    • 定义：质点A的动量对于点O的矩，为质点对于点O的动量矩即
    • 质点对某定点的动量矩对时间的一阶导数，等于作用力对同一点的矩 The first derivative of the moment of momentum of a particle to a fixed point with respect to time is equal to the moment of force to the same point
  • 动能定理 Kinetic energy theorem
    • 质点动能的增量等于作用在质点上力的元功 The increase in kinetic energy of a particle is equal to the elemental work of the force acting on the particle