Questions tagged [mathematics]

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31 views

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
82 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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28 views

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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19 views

Finding characteristic time required to reach steady state in the pump equation

Consider the pump equation $$\rho \frac{\partial w}{\partial t} = K' + \frac{\mu}{r} \frac{\partial }{\partial r} \left(r \frac{\partial w}{\partial r} \right)$$ Subject to $w(r=R,t)=0$, $w(r=0,t)$ is ...
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1answer
34 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
51 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
79 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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0answers
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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19 views

how to obtain solution of this bessel equation using Frobenius method

Given this equation: $$ \frac{1}{r}\frac{d}{dr}\bigg(r \frac{dT}{dr} \bigg) - \bigg(\frac{2h}{bk} \bigg)(T-T_a) = 0 $$ I can let $x=r\sqrt{(2h/bk)}$ and $z=T-T_a$ to obtain the bessel equation using ...
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4answers
80 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
46 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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16 views

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
35 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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27 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
33 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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20 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
37 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
21 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
57 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
92 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
42 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
74 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
62 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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19 views

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
67 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
114 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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0answers
29 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/...
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38 views

Mathematical transformation of a heading angle to a roll angle

I'm trying to understand a function in a SIMULINK example of a path following UAV simulation. The gist is that, the UAV Waypoint Follower block provides a required heading from a list of waypoints and ...
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1answer
15 views

Are Loop Closure Equations and Holonomic Constraints the same thing?

I'm reading a book on robotics, and it has a different section on each term. The way both concepts are worded and phrased mathematically make them seem like they both constrain the configuration space ...
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1answer
39 views

Bounds to prove exponential stablity for given Lyapunov function

Problem 3.6 in Khalil's Nonlinear Control: Use given Lypunov candidate function to prove that the origin is exponentially stable. The system is $$\dot{x}=\begin{bmatrix}x_2\\-h(x_1)-2x_2\end{bmatrix},...
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1answer
36 views

How much energy do mass drivers need to project 1lb of material 1km/second

I am working on a geoengineering project that, at the moment, seeks to use many mass drivers to project lunar regolith (lunar soil) or other materials into space to create targeted shading effects on ...
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4answers
63 views

Planes, lines and distances: looking for engineering problems

In a week from now, I am going to teach a one-time class to first-year engineering students about 3D geometry, more specifically: distances between points and lines/planes, and the common ...
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1answer
77 views

How to obtain plant parametric model of given system?

Consider the system: $$ y(s)=b\frac{e^{−sτ}}{s+a}u(s) $$ where a,b are unknown, constant parameters and $\ τ>0 $ is an unknown delay constant. How can I obtain a plant parametric model for this ...
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1answer
38 views

Interpreting Std Deviation

So I have a set of data, units purchased per month over a 4 or 5 year period. I have about 3000 different items, but here are 2 examples of what Ive done: Item 1: Mean 24 STDEVA 18 It has purchases ...
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2answers
426 views

How to calculate meters per pixel for a given camera?

I am stuck on this problem for a while: I have a square-shaped camera, with: 1000 pixels on vertical side 1000 pixels on horizontal side I want to know the number of meters per pixel depending of ...
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1answer
59 views

Impact of Gearbox on Motor Inertia

If you consider a motor attached to a spur gearbox with a reduction ratio of say $r=50:1$ which is then back-driven so that the motor acts as a generator, what would be the effective moment of inertia ...
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1answer
45 views

Deriving the ideal equation for sluice gate problems - incompressible inviscid fluid

I'm trying to figure this problem out, i know the correct answer, and i know the method, but for some reason i'm missing something and i'm just not getting there, any help would be greatly appreciated....
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1answer
39 views

How do I change the coordinate system from x-y to n-t or r-theta by using Matrix? [closed]

How do I change the coordinate system from two dimensional cartesian to two dimensional curve linear and polar by using Matrix?
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3answers
52 views

Why do we get singularities in a solutions while modelling a physical systems?

I wonder why do we get some times singularities (position to be infinity or velocity to be infinity) in the solutions while modelling a real system and in spite of taking all real parameter values of ...
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0answers
68 views

Help with Engineering Mathematics, Struggling to determine coefficients using methods detailed in this research paper

I am struggling with a curve fitting calculation below. the part I am stuck with is arguably the simplest part, which is determining the coefficients $\\K_3$ and $\\K_4$. It seems like it should be ...
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1answer
35 views

Question regarding calculation of angular velocity connected to coordinate transformation

So i need to calculate the angular velocity of the dark disk, $w^*_3$. In the master solution they state it is : $w^*_3 = w_3 + \overline{w_3}$ with : $w_3 = \frac{|\dot{r}|}{4a}$ $|\dot{r}| = v_a +...
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13 views

How to calculate new focal plane position when adding a lens to a lens system?

I am currently struggling with some lens equations. I hope this is the right place to ask such questions. What I'm trying to accomplish is to add a separate single lens to a camera setup and ...
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1answer
81 views

Changing fields from mathematics to control engineering [closed]

I did my undergraduate in maths and physics and will be working in control theory for my future job. Not to my surprise, my engineering background is rather lacking. I have taken a look at materials ...
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3answers
62 views

Calculate area of mesh?

I have expanded steel mesh that I use to make garden cages: I would like to know how much sunlight the mesh blocks. I think I need to calculate the area that the mesh takes up (per square inch) and ...
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3answers
319 views

Should Engineers Understand Equations without Relying on Derivations?

As I've progress through my undergraduate engineering program, I've noticed a shift away from physical intuition - understanding why certain phenomena or equations make sense because of basic patterns ...
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2answers
108 views

finding the center of rotation between 2 rigid bodies

I feel a little lost. I think my problem is quite simple, but unfortunately, my knowledge of math is also simple. I have two rigid bodies that move relative to each other. I know two points of each ...
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0answers
17 views

How to sample Mean-Time-To Failure values from a Weibull Distribution with shape 1.5?

I have a mean time to failure (MTTF) recorded from 100 systems which is 6.5 years. The shape parameter of my component is given with k = 1.3 (based on a list the from literature). Now I want to ...
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1answer
37 views

Help with determining the dimension change in the xyz direction of a component under a load?

I'm stuck on this question. I got the first part right which is to work out the dimension change in the x direction but I got the y and z directions wrong. I had to submit this online and it doesn't ...
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0answers
35 views

Solving Hertz Impact ODE with Simulink

I have a question about modelling a nonlinear 2nd order ODE for an impact of a sphere on a thin plate in Simulink. Depending on the solver and solver options, my results in Matlab vary a lot. Some are ...