LIke's blog

week 6-7 torque τ=Fl=Icmαcm\tau = Fl = I_{cm}\alpha _{cm}τ=Fl=Icm​αcm​ angular acceleration Ftan=m1atan,atan=razF_{tan} = m_1a_{tan},a_{tan}=ra_zFtan​=m1​atan​,atan​=raz​, l = r τ=Ftanr=m1atanr=m1r2az\tau = F_{tan}r = m_1a_{tan}r = m_1 r^2 a_zτ=Ftan​r=m1​atan​r=m1​r2az​ τ=∑τ1=∑m1r2az=Iaz\tau = \sum \tau _1 = \sum m_1 r^2 a_z = I a_zτ=∑τ1​=∑m1​r2az​=Iaz​ rigid body rotation about moving axis–axis choosing choose COM choose instant center translation and rotation τ=Ia\tau = Iaτ=Ia is under ...

line int. over curve CCC -> line int. of a vector field FFF over curve CCC 123相当于把一系列点串起来，此时形成了curve $C$。然后限定 Field $F(x,y,z)$中xyz满足curve $C$的轨迹把轨迹方程里面所有点的信息_输入_到F中, 方程替代自变量 F⃗(r⃗(t))=M(x,y)i^+N(x,y)j^\vec{F}(\vec{r}(t)) = M(x,y)\hat{i} + N(x,y)\hat{j} F(r(t))=M(x,y)i^+N(x,y)j^​ forward direction is defined by r⃗(t)\vec{r}(t)r(t) Unit Tangent vector 1234imagine the definition in geometry. first is the distribution on s, which is scalar second is by definition in velocity, $v$(velocity) point ...

attention polar range of θ\thetaθ is [0,π][0, \pi][0,π], if change to 2θ2\theta2θ, then range of θ\thetaθ is [0,π2][0, \frac{\pi}{2}][0,2π​] 联系图像，注意自变量取值变化 积分失败立马检查积分原式，大概率漏了jacobian或者n-1次项 在连续函数中fxy=fyxf_{xy} = f_{yx}fxy​=fyx​,所以在积分时候，积分θ,r\theta, rθ,r顺序无所谓，关注积分取值即可 -[ ] triple 立体图形是灵活的…，第一步一定选择光滑且投影上下重合那个面，太妙了兄弟，第一次我直接切割分布计算浪费时间 根据形状选择合适的积分顺序是技术 general 抄写漏项 积分容易漏积，对y积分记得把所有类常数都添上一个y 时刻写上取值，我曾经多积一次 开始积分之前，先核实三个取值区间是否是正确的 三角函数的积分明显出错率比较高，请及时解决 表达式写对，积分写对 double integral in catisian coordi ...

Null(A) 齐次线性方程组 Ax=0的通解 homogeneous solution for Ax=0Ax = 0Ax=0 n(A) n(A)=dim(Null(A))n(A) = dim(Null(A))n(A)=dim(Null(A))

basic input a vector, output a vector it is a type of transformation, so think it in moving way the origin should not change, or it will become “affine transformation”(仿射变换) the grid should keep parallel and evenly distributed 【平行且等距分布】after the transformation, so that can be called as “linear” transformation do strech, spin(trigonometric), projection(object, light, shadow), change the dimension(not invertible) here, the transformation is done by matrix matrix is the operater for the basis ...

Time line April 11th (Thr) 早上是六点二十分在乐天集合的，在那之前我们加急完成了三辆车的机械部分的任务，十号的安装我没有参与，有人是通宵的，任务是十分紧的 p.s. 我是九号参与安装，熬到了凌晨一点多，然后同一天，这个hexo的博客诞生了———一个极端情况下的疯狂想法 看着66*66*70的航空箱，校徽与过岗龙(dragopass)被装上了货拉拉的车，去往福建福州的RMUL比赛打响了 早餐吃的肯德基，吃完后四辆网约车到坪山站。周边看到了云巴这种类轻轨的交通方式，坪山站可能在扩建。打印报销凭条后过完安检——睡觉。上了D388——睡觉，试图写turtle，不清醒，无果。 一点半多准时到福州南。体验了类似于探鱼的那种店作为午餐，入住木兰澜苑（MLLY），名字莫名其妙的旅店，但是住的是舒服的。柔和的灯光布景，大面积，我喜欢。 晚上去福建理工大学报道，我们的车调了挺久才去裁判区进行检录，那时我们是最后一个队伍而且超时了，但是遇到一个很好的referee，耐心的检测我们的车辆是否符合规则。检录时候遇到许多问题，一一记下，熬夜修改，今天晚上xyf 13号五点才回MLLY ...

need want to type math stuff efficiently in my blog preparation vscode (editing) and texlive (rendering) reference VScode + latex Math Snippet inner product and orthogonal highly relative

more to say you see | number |, you see || vector || notation of xTyx^TyxTy another way to denote inner prodoct, i.e. dot product def. of euclidean length distance from origin to arror end. Sum of each component’s square and take square root def. of distance distance of arbitary two vector scalar product of vector length simply times a scalar def. ⊥\perp⊥ vector in Rn\mathbb{R}^nRn inner product is zero 勾股定理 same in geometric def. of projection with dir. vector the projection of v on to u,Proj ...

前期指引 AI guide Here’s a breakdown of what you’ll learn in each step: Node.js Basics: How to install Node.js, run Javascript code, and use npm to manage packages. Markdown: How to format text with headers, bold, italics, links, images, and more. Hexo Basics: How to install Hexo, create a new blog project, write blog posts in Markdown, use themes to customize your blog’s look, and deploy your blog to a hosting platform. Yuan yue Guide 小白向blog搭建指南 [Yuanyue file]（） butterfly手把手(CSDN) butterfly blo ...

Welcome to Hexo! This is your very first post. Check documentation for more info. If you get any problems when using Hexo, you can find the answer in troubleshooting or you can ask me on GitHub. Quick Start Create a new post 1$ hexo new "My New Post" More info: Writing Run server 1$ hexo server More info: Server Generate static files 1$ hexo generate More info: Generating Deploy to remote sites 1$ hexo deploy More info: Deployment