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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Basic Motion of the Rigid Body

Translation is the motion of a rigid body, not a particle, as we all know the fact that the rigid body is the cluster system of particles. As shown in Fig. 8.1, a rigid body is lying on a desk undergoing a horizontal force. This object can move linearly in the desk surface, so clearly, its motion is called translation. However, what’s the actual definition of translation? Normally, we can draw a straight line on the object in the initial state, if after a while the current position of the line is always parallel to the initial line, then the motion of the object is defined as translation.

Let’s look at another example shown in Fig. 8.2. A rigid body is tied by two slender ropes, which are hung on the ceiling. The two parallel bars can rotate on the ceiling, and the rigid body can sweep with the rotation of the two ropes. We examine the motion law of one point $A$ on the rigid body, whose orbit is really a portion of a circle. Another point $B$ is also in a circular motion. However, in this case, the motion type of the rigid body in Fig. $8.2$ is translation. We also analyze a straight line, such as $A B$. After the rigid body moves to another position, such as the virtual line in Fig. 8.2, the current straight line is parallel to $A B$. Therefore, although an arbitrary point on the rigid body is in a circular motion, the motion of the total system is surely translation.

It’s natural to see that the velocities and accelerations of point $A$ and $B$ are both equal, as the length of $A B$ on the rigid body does never change. As a result, we arrive at the conclusion that every point on a rigid body in translation has the same velocity and acceleration. For two arbitrary points, one has
\begin{aligned} &v_{A}=v_{B} \ &a_{A}=a_{B} \end{aligned}

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Rotation on a Fixed Axis

As shown in Fig. 8.3, if we impose a moment on a door, the door will be closed with respect to a fixed axis. This type of motion is also a basic motion, termed as rotation with respect to a fixed axis. In this rotation process, there always exists a fixed axis on the rigid body. This type of motion takes some special features. If we look through the positive direction of $z$-axis in Fig. 8.3, we can find the orbit of an arbitrary point on the rigid body in rotation, which is actually a circle.

To depict the motion of the rigid body, we introduce the angular displacement $\varphi$, whose sign also obeys the right-hand screw law. The angular velocity can be defined as
$$\omega=\lim _{\Delta t \rightarrow 0} \frac{\Delta \varphi}{\Delta t}=\dot{\varphi} .$$
The angular velocity can also be related with the frequency via
$$\omega=2 \pi f .$$
Introducing the concept of rotation velocity $n$ with the unit of $1 / \mathrm{min}$, one has

$$\omega=\frac{2 \pi n}{60}=\frac{\pi n}{30} .$$
Similarly, the angular acceleration can be further defined as
$$\varepsilon=\lim _{\Delta t \rightarrow 0} \frac{\Lambda(t)}{\Delta t}=\dot{\omega}=\ddot{\varphi} .$$

# 理论力学代写

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Basic Motion of the Rigid Body

$$v_{A}=v_{B} \quad a_{A}=a_{B}$$

## 物理代写|理论力学作业代写Theoretical Mechanics代考|Rotation on a Fixed Axis

$$\omega=\lim {\Delta t \rightarrow 0} \frac{\Delta \varphi}{\Delta t}=\dot{\varphi} .$$ 角速度也可以通过以下方式与频率相关 $$\omega=2 \pi f$$ 介绍旋转速度的概念 $n$ 以 $1 / \min {1}$ 个个有
$$\omega=\frac{2 \pi n}{60}=\frac{\pi n}{30} .$$

$$\varepsilon=\lim _{\Delta t \rightarrow 0} \frac{\Lambda(t)}{\Delta t}=\dot{\omega}=\ddot{\varphi} .$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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