Questions tagged [mathematics]

For engineering questions involving mathematics. For pure mathematics problems, please visit our sister site Mathematics Stack Exchange.

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Automatic Tissue Dispenser

My father is a software engineer and yesterday he asked me a question to test me, that I cannot, for the life of me, seem to figure out. He told me that I need to make a tissue paper dispenser that, ...
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1answer
34 views

Calculate effect of drag on ball in motion

So I’ve been trying to work out the range of a ball that has been projected by two spinning discs please when accounting for drag- This is what I got so far: $V=V\cos\theta$, $T=2V\sin\theta/g$ , and $...
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46 views

How to calculate forces for most appropriate electric engine for soft sand? [duplicate]

I'm super new to this topic I'm posting here so please forgive the nursery question and content. I'm hoping to use any answers to help me begin my research and investigation on what I need to learn. I'...
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Is there an equation that can automatically tune a PID controller?

Is there an equation that can automatically tune PID controllers? or do I have to do manually/make an AI to do it for me?
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compute nodes and members according to stiffness matrix of truss (inverse the direct stiffness method)

I am familiar with the direct stiffness method (truss), and programmed it from scratch in Java. The member stiffness matrix is determined by any link (member) and the nodal coordinates. The global ...
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2answers
59 views

Is pursuing a Maths degree useful in engineering [closed]

whilst this is an open ended question, and not really 'on topic' for the site, I couldn't figure anywhere better to post it than on an engineering forum! (I can delete it after I receive an answer if ...
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How can I map a global spherical position of a central normal vector to the rotation of 2 perpendicular motors?

I have a machine that rotates two concentric frames. The outer frame has a motor that rotates it relative to the global y-axis, and the inner frame has a motor that rotates it about the outer frame's ...
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1answer
44 views

Raise/Lower 350lb Sawmill Head 12v Motor Specs

I am new to this site and have a problem to solve in an area that I’m pretty lost in. I can usually figure stuff out with the help of the internet and some digging but not getting real traction so ...
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Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$ \dot{x}(t) = Ax(t) $$ is stable ...
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1answer
72 views

Can you offer real-world examples of logarithm use? [closed]

Can you offer real-world examples of logarithm use? An example of a real-world layman application of logarithms is understanding amplifier power ratings. For example a 30 watt amp is not one third as ...
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65 views

How do rollercoaster designers calculate the ideal curve?

I've been looking into rollercoaster track designs and wondered how they mathematically calculate the ideal curves to fit some specific layout without creating excessive Gs or other rider discomfort ...
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1answer
37 views

Resolving the forces into components [closed]

okay so I am really struggling to see how to resolve the Normal reaction force and Weight into the r and theta direction please? Why is it that the angle is taken to the left of N and right of mg ...
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Question regarding the extreme wind velocity distribution in Eurocode

Above is the definition of the probability factor from Eurocode 1-4. It is used in context of calculating the extreme wind load on a building. Ignoring some other factors, it is used as follows: $$v_b ...
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1answer
53 views

FE Exam practice: "How many years until you're a millionaire?" [closed]

One of the early questions in the NCEES FE Industrial/Systems Exam studyguide has a solution that I can't decipher. The question is as follows: ...
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Scalability in the context of optimization and control systems

I am having a hard time trying to make sense of the phrase "Scalable optimization". I read from a few papers discussing that some global optimization solvers like BARON, ANTIGONE, etc. do ...
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1answer
122 views

Infinitesimal Strain Tensor in Cylindrical Coordinates

How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to ...
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1answer
55 views

Stretch in Infinitesimal strain theory

In the picture above we have the expression of stretch with respect to strain tensor, but in case of infinitesimal strain theory, we take stretch equal to 1+T.E.T I don't understand why by taking ...
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2answers
81 views

What's the name of the calculus used to make smooth transitions in roads?

So I'm not actually an engineer, I'm a novice computer programmer but I think in order to solve a problem I have I'm going to need some help from the world of engineering. I remember in high school ...
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1answer
227 views

Determine the parameters for this given nyquist plot

I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one: My thoughts so far: Replace $$s \rightarrow j\omega$$, $$G(...
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Could tic-mark labels on a graph have individual decimal digits with different signs?

I'm currently looking at a graph (figure 5 of Ede (1967), "Advances in Free Convection", in Hartnett and Irvine (eds.), Advances in Heat Transfer vol. 4, New York: Academic Press), in which ...
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3answers
91 views

Statically determinate system

The exercise is taken from linear algebra and its applications, prof. G. Strang Exercise 2.4.8 Truss I have already found that: m=n=8 → system is statically determinate, therefore solvable by ...
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1answer
62 views

Obtaining equation from real life

As I was studying about differential equation,then I got a question in my mind that we are taking out general solutions for a differential equation. Like for example - Q) $\frac{dy}{dx} = \left[\frac{...
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How to judge the character and sign of a dislocation?

I do understand that $ \mathbf b||\mathbf t$ for screw dislocation but I am unable to judge the sign of the dislocation. Again if $\mathbf b \perp \mathbf t$ how do I judge its sign? Any formula which ...
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Temperature Question

A thermistor, which has a Negative Temperature Coefficient (β) of 3300 (K) and a resistance ($R_o$) of $10\text{ k}\Omega$ at a reference temperature of 21ºC, is used to measure the temperature of an ...
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2answers
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Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of ...
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2answers
116 views

How to Derive the Differential Form of the Contintuity Equation

The book "Gas Turbine Engineering Handbook" by Boyce, on p. 117 states, the continuity equation, $ \dot m = \rho A V $, has as its differential form, $ 0 = \frac{d\rho}{\rho} + \frac{dA}{A} ...
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Are gas distribution networks tree-like?

I was wondering, if it is justified to say, that gas distribution network graphs (primarily in Europe) are typically tree-like. By gas distribution networks I mean municipal and regional distribution ...
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1answer
108 views

How to calculate the torque for motors for a Core XY movment?

I am trying to design a simple setup that follows the core XY movement shown: I have been researching the statics behind this movement in order to calculate the minimum torque for the motor so I ...
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1answer
150 views

Does Finite Element Method use direct stiffness method?

Does Finite Element Method use direct stiffness method? Or it is another mathematical method? We definitely use direct stiffness method to solve frames. FEM is based on entirely this or depending on ...
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2answers
160 views

How high will a flywheel catapult launch a payload?

First off, this is not a homework question or anything like that. I'm trying to build a catapult to launch a payload using a flywheel as an energy device! It goes like this: The flywheel spins up to ...
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20 views

multidimensional function for object description

I want to simulate a bow tie antenna and build it up with a function. so far i have managed to create a piece of cake with sin and cos. Now I would like to expand the function and round off the ...
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4answers
139 views

Swing safety: maximum load of beam (supported at one end, free with load on the other)

My husband and his dad built a fort for our two boys. Coming off of one side of the fort is a 4x6 wooden beam with a tire swing attached at the end. It is supported on one side by the fort, but not ...
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1answer
68 views

Is the identity matrix a tensor?

If we multiply the identity matrix by any vector or a matrix, then the result is the vector or the matrix themselves (like a mirror). Tensors represent physical quantities, so if it wasn't a physical ...
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RF Engineering - Cascading a 3 Port S-Parameter Network into a 4-Port S-Parameter network

I have been trying to cascade a 3-port scattering parameter network into a 4-port scattering parameter network that will ultimately be terminated by another 3-port network (as can be seen below). The ...
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1answer
44 views

Gaps in derivation of thermodynamic property equations

If $h=h(T, P)$. Does $ dh = c_pdT + \left[v - T\left(\frac{\partial v}{\partial T}\right)_P \right]dP \Rightarrow h_2 - h_1 = \int_{T_1}^{T_2} c_pdT + \int_{P_1}^{P_2}\left[v - T\left(\frac{\partial v}...
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41 views

How does NASA's QueSST X-59 jet work?

The QueSST (Quiet Supersonic Transport) is a project to create a more diffuse sonic boom in order to use supersonic flight commercially without the usual abrupt 1~2 psf pressure spike damaging the ...
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1answer
66 views

Calculating features of a 3 phase power timeseries

I have data from a number of high frequency data capture devices connected to generators on an electricity grid. These meters collect data in ~1 second "bursts" at ~1.25ms frequency, ie. ...
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33 views

Using complementary filter in rotation matrix

I am using accelerometer and gyroscope and try to compensate earth gravity. I figured out use of complementary filter, that calculates pitch and roll angle. On account of compensating gravity I am ...
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3answers
40 views

Placing an accelerometer on arbitrary position and define this as the new coordinate system

I'm working on a small home project and I'm looking to use an accelerometer for tilt sensing. I would like to be able to place it anywhere on the object. If I place it in a way that the coordinate ...
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1answer
25 views

How do I compute the torque in ft lbs to turn a screw and move a 2000 lb weight?

I am having trouble locating the calculations for finding the torque, in ft/lbs, required to turn a 1/2" screw with 13 threads per inch and pull 2000lbs 6 inches. .
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1answer
386 views

How can I implement S-curve motion profile on mobile robotic platform / wheeled robot?

I want to plan a robot's motion according to an S curve profile. I am following the article mention below, which contains basics related to S curve motion profiles in robotic platforms. https://www....
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30 views

Is a pyramid considered axisymmetric? Why so?

I read a source, I will not reference the source on this platform. They stated a pyramid is axisymmetric. Can you explain why if yes?
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1answer
340 views

Hansel-Spittel equation parameter determination

I am currently learning how to determine the Hansel-Spittel equation parameters. The equation has following form: $$\sigma= A \cdot e^{m_1\cdot T}\cdot(\epsilon^{m_2})\cdot \exp\left(\frac{m_4}{\...
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1answer
60 views

Air - rectangular membrane system vibration and natural frequency

I'm struggling with the following problem: The boundary conditions are $w(x,y) = 0$ around the edges. I am supposed to find the natural frequencies of the system as a whole, and find the solution ...
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1answer
132 views

Help understanding a control system represented by coefficients of theta?

I've been working with control systems and transfer functions recently, but I've come across a format that I haven't seen before using coefficients of theta, and I can't find any information about it. ...
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0answers
68 views

Converting nonlinear system into equivalent nonlinear of the Byrnes-Isidori normal form

I have a nonlinear system (Ball & Beam) which is described by the following equations of motion: $$ \ddot{y} + \frac{mg}{a} \sin(θ) -\frac{m}{a}y\dot{θ}^2 = 0 $$ $$ \ddot{θ} + \frac{2m}{b}y\dot{...
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Factoring in Efficiency in Equations

A pretty simple question, but one that's weirdly confusing me: I'm working with an equation for total water demand (Q) were w is the allowance for water wasted. w is typically 30%. Most books ...
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1answer
84 views

Input-output representation to state space

How do you create a state space representation of the following input/output equation: $$ \dot{y} = -ky + u + a\sin(ωt) $$ where the parameters $k$, $a$, and $ω$ are unknown. The end goal is to ...
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1answer
162 views

linearizing a non linear state space equation

I have this 1-DOF helicopter simulator. The motor's armature resistance is $R$, inductance $L$ and motor constant $K$ and reaction torque on the motor shaft is $τ$. $T$ is equal to $k_1w_2^2$ and $...
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114 views

Finding transformation of forces and moments

I have two sets of forces and moments, measured by two 6 DOF force/torque sensors at position A and B on a robot arm (B at end effector). My goal is to use this measurements to relate the forces/...