Questions tagged [mathematics]

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14 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
29 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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21 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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19 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
36 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
20 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
44 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
62 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
40 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
71 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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56 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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17 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
66 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
108 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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28 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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37 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
14 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
76 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
240 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
54 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
34 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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25 views

What's the most anisotropic material? Is there a dense stiffness matrix?

The stiffness (aka. tangent modulus of the stress) can be represented as a symmetric 6-by-6 matrix, i.e. it has 21 independent components in the most general case. In the linear case, this matrix is ...
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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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14 views

Reformulate navier-stokes in terms of perturbation

I am reading this paper and trying to understand on page 14-15, First it rewrites Navier-Stokes in terms of a ''zero order problem'', and where $u_i = \mathscr{U}_i + u_i'$ , where $U_i$ is the base ...
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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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12 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
80 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
58 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
280 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
100 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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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 ...
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44 views

Distance travelled at articulation point of turning vehicle

Problem outline: I'm trying to figure out the distance travelled at the articulation point of a turning vehicle with 4 driven wheels (each wheel houses a motor and can all rotate at different RPMs). ...
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2answers
43 views

What is the engineering way to describe a factory / manufacturing plant system in a formel and mathematical way

I am interested in mathematically describing as well as formalising a manufacturing plant so that other people in the engineering field understand how the system works. I am not from the engineering ...
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2answers
60 views

Can a simple application of two forces have two different outcomes on a rigid body?

[Summary: If two forces are such that the component of one of these forces forms a couple with the other, than which of the two cases (obtaining resultant via adding forces or obtaining moment and a ...
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1answer
88 views

LED Lumen Calculations

I am using an LED as a point source for a school project. I have two questions in regards to the LED(s). I know that light follows the inverse square law when measuring perceived brightness, but all ...
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1answer
212 views

Gyroscope/Powerball gearing system for bikes?

There is an interesting and potentially useful property to do with the procession of Gyroscopes, as well as devices like the "Powerball" toy. When the gyroscope is rotating (Ws) and then force is ...
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2answers
72 views

Differential equation

What are boundary conditions and initial conditions with respect to differential equation? Do they mean the same for partial differential equation? How to BC and IC vary for different types of PDE?
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2answers
110 views

How do enginners build highway interchanges ? Are highway interchanges build based on a mathematical theory such as braids and knots theory?

I am trying to find how do enginners build roads especially highway interchanges. Are they relying on any topology theories such as braids and knots theory? Is there any connection or link between ...
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37 views

Engine power and torque of a vehicle

Having the Power/Torque-RPM curves of a vehicle, how can we derive the engine power equation and the torque out of these curves with respect to time?
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1answer
102 views

Get results of output for each one value of the input - MATLAB ODE

I am simulating a mass - damper - system in Matlab and I have the following vector (1x100) as input to my system: ...