19th Ave New York, NY 95822, USA

# 物理代写|理论力学代写Theoretical Mechanics代考|PHYS5301 Velocity and Acceleration

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

## 物理代写|理论力学代写Theoretical Mechanics代考|Velocity and Acceleration

The motion of a mass point is characterized by:
position vector : $\mathbf{r}(t)$,
velocity vector: $\quad \mathbf{v}(t)=\dot{\mathbf{r}}(t)$,
acceleration vector: $\mathbf{a}(t)=\ddot{\mathbf{r}}(t)$.
Higher time derivatives do not interest us in mechanics; very often they even fail to exist because in many realistic cases the acceleration is not a continuous function of time.

The typical task for mechanics consists of the calculation of the path line (trajectory) $\mathbf{r}(t)$ on the basis of a given acceleration $\mathbf{a}(t)=\ddot{\mathbf{r}}(t)$. For this purpose one has obviously to integrate $\mathbf{a}(t)$ twice with respect to time. After each integration an integration constant appears which remains undetermined unless we have two initial conditions at our disposal to fix these constants. In this connection let us assume that we know the velocity and the position of the mass point (particle) at a certain time $t_0$, i.e.
$\mathbf{a}(t)$ for all $t, \mathbf{v}\left(t_0\right)$, and $\mathbf{r}\left(t_0\right)$
are given. Then the velocity of the particle is determined by
$$\mathbf{v}(t)=\mathbf{v}\left(t_0\right)+\int_{t_0}^t d t^{\prime} \mathbf{a}\left(t^{\prime}\right)$$
and the position vector by:
$$\mathbf{r}(t)=\mathbf{r}\left(t_0\right)+\mathbf{v}\left(t_0\right)\left(t-t_0\right)+\int_{t_0}^t\left[\int_{t_0}^{t^{\prime}} d t^{\prime \prime} \mathbf{a}\left(t^{\prime \prime}\right)\right] d t^{\prime}$$

## 物理代写|理论力学代写Theoretical Mechanics代考|Simple Examples

(a) Mass Point on a Straight Line
We can describe the motion without referring to any special system of coordinates. If $\mathbf{c}$ is a vector in the direction of the motion and $\mathbf{b}$ a vector perpendicular to it then we can write for the position vector of the mass point (Fig. 2.4):
$$\mathbf{r}(t)=\mathbf{b}+\alpha(t) \mathbf{c} .$$
From this, the respective time derivatives give us the velocity and acceleration:
$$\mathbf{v}(t)=\dot{\alpha}(t) \mathbf{c} ; \quad \mathbf{a}(t)=\ddot{\alpha}(t) \mathbf{c} .$$
(b) Uniform Straight-Line Motion
Therewith it is meant the most simple form of motion, namely the one without any acceleration:
$$\mathbf{a}(t)=0 ; \quad \mathbf{v}(t)=\mathbf{v}_0 \quad \text { for all } t .$$

## 物理代写|理论力学代写THEORETICAL MECHANICS代 考|VELOCITY AND ACCELERATION

$$\mathbf{v}(t)=\mathbf{v}\left(t_0\right)+\int_{t_0}^t d t^{\prime} \mathbf{a}\left(t^{\prime}\right)$$

$$\mathbf{r}(t)=\mathbf{r}\left(t_0\right)+\mathbf{v}\left(t_0\right)\left(t-t_0\right)+\int_{t_0}^t\left[\int_{t_0}^{t^{\prime}} d t^{\prime \prime} \mathbf{a}\left(t^{\prime \prime}\right)\right] d t^{\prime}$$

## 物理代写|理论力学代写THEORETICAL MECHANICS代 考ISIMPLE EXAMPLES

$a$ 直线上

Fig. 2.4:
$$\mathbf{r}(t)=\mathbf{b}+\alpha(t) \mathbf{c} .$$

$$\mathbf{v}(t)=\dot{\alpha}(t) \mathbf{c} ; \quad \mathbf{a}(t)=\ddot{\alpha}(t) \mathbf{c} .$$
bUniform Straight-Line Motion

$$\mathbf{a}(t)=0 ; \quad \mathbf{v}(t)=\mathbf{v}_0 \quad \text { for all } t$$

## 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。