Theoretical mechanics Chapter &, Compositive motion of a particle
1 Theoretical mechanics
理论力 41人
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Chapter 8: Compositive motion of a particle D88-1 Concept of compositive motion of a particle 心§8-2 Theorem of composition of velocities of a particle D88-3 Theorem of composition of accelerations when the convected motion is translation 88-4 Theorem of composition of accelerations when the convected motion is rotation D Lesson for problem solving
3 §8–1 Concept of compositive motion of a particle §8–2 Theorem of composition of velocities of a particle §8–3 Theorem of composition of accelerations when the convected motion is translation §8–4 Theorem of composition of accelerations when the convected motion is rotation Lesson for problem solving Chapter 8: Compositive motion of a particle
第八章点的合成运动 心§8-1点的合成运动的概念 §8-2点的速度合成定理 §8-3牵连运动为平动时点的加速度合成定理 §8-4牵连运动为转动时点的加速度合成定理 习题课
4 §8–1 点的合成运动的概念 §8–2 点的速度合成定理 §8–3 牵连运动为平动时点的加速度合成定理 §8–4 牵连运动为转动时点的加速度合成定理 习题课 第八章 点的合成运动
Kinematics In the previous two chapters, we have considered the motion of a particle or a rigid body with respect to a system of fixed coordinate axes. In practice however, we often observe the motion with respect to a moving body. For example, we observe the motion of an flying airplane from a moving car, or observe the motion of raindrops from a traveling train. Why do obtain different results when we observe the motion a object on different coordinate systems or reference objects? It is known that there may exist relationship between two different objects. Next, we are going to study the relationship between the motions of an object and the reference object. First of all, we begin with the introduction of some concepts 88-1 concept of compositive motion of a particle 1. Coordinate system 1) Static coordinate system: A coordinate system fixed to the earth ground is called Static coordinate system SCs). 2) Moving coordinate system: A coordinate system fixed to a moving object relative to the earth ground is called moving coordinate system MCs). Forexample, a running car
5 §8-1 concept of compositive motion of a particle 1．Coordinate system： 1) Static coordinate system: A coordinate system fixed to the earth ground is called Static coordinate system (SCS). 2) Moving coordinate system: A coordinate system fixed to a moving object relative to the earth ground is called moving coordinate system (MCS). For example, a running car. In the previous two chapters, we have considered the motion of a particle or a rigid body with respect to a system of fixed coordinate axes. In practice, however, we often observe the motion with respect to a moving body. For example, we observe the motion of an flying airplane from a moving car, or observe the motion of raindrops from a traveling train. Why do obtain different results when we observe the motion a object on different coordinate systems or reference objects? It is known that there may exist relationship between two different objects. Next, we are going to study the relationship between the motions of an object and the reference object. First of all, we begin with the introduction of some concepts
运动学 前两章中我们研究点和刚体的运动,一般都是以地面为参考 体的。然而在实际问题中,还常常要在相对于地面运动着的参 考系上观察和研究物体的运动。例如,从行驶的汽车上观看飞 机的运动等,坐在行驶的火车内看下雨的雨点是向后斜落的等 为什么在不同的坐标系或参考体上观察物体的运动会有不 同的结果呢?我们说事物都是相互联系着的。下面我们就将研 究参考体与观察物体运动之间的联系。为了便于研究,下面先 来介绍有关的概念。 §8-1点的合成运动的概念 坐标系: 1静坐标系:把固结于地面上的坐标系称为静坐标系简称静系。 2动坐标系:把固结于相对于地面运动物体上的坐标系, 称为动坐标系,简称动系。例如在行驶的汽车
6 §8-1 点的合成运动的概念 一．坐标系： 1.静坐标系：把固结于地面上的坐标系称为静坐标系,简称静系。 2.动坐标系：把固结于相对于地面运动物体上的坐标系， 称为动坐标系，简称动系。例如在行驶的汽车。 前两章中我们研究点和刚体的运动，一般都是以地面为参考 体的。然而在实际问题中，还常常要在相对于地面运动着的参 考系上观察和研究物体的运动。例如，从行驶的汽车上观看飞 机的运动等，坐在行驶的火车内看下雨的雨点是向后斜落的等。 为什么在不同的坐标系或参考体上观察物体的运动会有不 同的结果呢？我们说事物都是相互联系着的。下面我们就将研 究参考体与观察物体运动之间的联系。为了便于研究，下面先 来介绍有关的概念
Kinematics 2. Moving point: a moving point under studying 3. Three kinds of motion and their velocities and accelerations 1)Absolute motion: motion of the moving point relative to the SCS. Motion of 2)Relative motion: motion of the moving point relative to the MCS. particle For example, motions of a person in a running bus 3)Convected motion: motion of the MCs relative to the SCS. Motion of a For example, motion of a running care relative to the earth ground rigid body The velocity and acceleration of the moving point in its a bsolute motion are called absolute velocity va and absolute acceleration The velocity and acceleration of the moving point in its relative motion are called relative velocity vr and relative acceleration ar The velocity and acceleration of the convected point in its absolute motion are called convected velocity Vand convected acceleration a convected point: the point in the mcs coinciding with the moving point at any instant of time. Image that the moving point were fixed to the MCs and moved together with the MCs. Such a point in the Mcs is called convected point 7
7 3．Three kinds of motion and their velocities and accelerations 1) Absolute motion：motion of the moving point relative to the SCS. 2) Relative motion：motion of the moving point relative to the MCS. For example, motions of a person in a running bus 3) Convected motion：motion of the MCS relative to the SCS. For example, motion of a running care relative to the earth ground. The velocity and acceleration of the moving point in its absolute motion are called absolute velocity and absolute acceleration The velocity and acceleration of the moving point in its relative motion are called relative velocity and relative acceleration The velocity and acceleration of the convected point in its absolute motion are called convected velocity and convected acceleration aa ve ae vr ar va convected point: the point in the MCS coinciding with the moving point at any instant of time. Image that the moving point were fixed to the MCS and moved together with the MCS. Such a point in the MCS is called convected point. Motion of a particle Motion of a rigid body 2. Moving point：a moving point under studying
运动学 .动点:所研究的点(运动着的点)。 三.三种运动及三种速度与三种加速度。 1.绝对运动:动点对静系的运动。 点的运动 2.相对运动:动点对动系的运动。 例如:人在行驶的汽车里走动。 3.牵连运动:动系相对于静系的运动刚体的运动 例如:行驶的汽车相对于地面的运动。 绝对运动中动点的速度与加速度称为绝对速度V与绝对加速度aa 相对运动中动点的速度和加速度称为相对速度W与相对加速度an 牵连运动中牵连点的速度和加速度称为牵连速度ve与牵连加速度ae 牵连点:在任意瞬时,动坐标系中与动点相重合的点,也就是 设想将该动点固结在动坐标系上,而随着动坐标系一起运动时 该点叫牵连点
8 三．三种运动及三种速度与三种加速度。 １．绝对运动：动点对静系的运动。 ２．相对运动：动点对动系的运动。 例如：人在行驶的汽车里走动。 ３．牵连运动：动系相对于静系的运动 例如：行驶的汽车相对于地面的运动。 绝对运动中,动点的速度与加速度称为绝对速度 与绝对加速度 相对运动中,动点的速度和加速度称为相对速度 与相对加速度 牵连运动中,牵连点的速度和加速度称为牵连速度 与牵连加速度 aa ve ae vr ar va 牵连点：在任意瞬时，动坐标系中与动点相重合的点，也就是 设想将该动点固结在动坐标系上，而随着动坐标系一起运动时 该点叫牵连点。 点的运动 刚体的运动 二．动点：所研究的点（运动着的点）
Kinematics 4. Guideline for selection of moving point: In general, the contact point between the drive and driven objects is usually selected as moving point, which moves relative to both SCS and MCs 5. Guideline for MCS selectio A MCS Should be a coordinate system(object)on which the trajectory of the moving point is known or clear Explanation of the concepts by examples Moving point: Point a on rod aB MCS: Fixed to cam C′ SCS: Fixed to the ground
9 Explanation of the concepts by examples: 4. Guideline for selection of moving point : In general, the contact point between the drive and driven objects is usually selected as moving point, which moves relative to both SCS and MCS. 5． Guideline for MCS selection: A MCS should be a coordinate system (object) on which the trajectory of the moving point is known or clear. Moving point: MCS: SCS： Point A on rod AB Fixed to cam Ｏ' Fixed to the ground
动学 四.动点的选择原则: 一般选择主动件与从动件的连接点,它是对两个坐标系都有 运动的点。 五.动系的选择原则: 动点对动系有相对运动,且相对运动的轨迹是已知的, 或者能直接看出的。 下面举例说明以上各概念: 动点:AB杆上A点 动系:固结于凸轮O上 静系:固结在地面上 10
10 下面举例说明以上各概念： 四．动点的选择原则： 一般选择主动件与从动件的连接点，它是对两个坐标系都有 运动的点。 五．动系的选择原则： 动点对动系有相对运动，且相对运动的轨迹是已知的， 或者能直接看出的。 动点： 动系： 静系： AB杆上A点 固结于凸轮Ｏ'上 固结在地面上