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Questions tagged [mathematics]

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Method to calculate required gear size and teeth size for a rack system for a certain amount of travel?

high school amateur engineer- and first-time poster- here. I'm making a Nerf automatic springer system, and I want to model it. However, I don't know what size rack and gear system I need. I need 60 ...
Tom Foolery's user avatar
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Confusion in deriving von Karman equation for strip rolling

In the derivation for von Karman equation for metal strip rolling, an infinitesimal element is chosen as shown in the picture above. The equilibrium equation for the element is as follows: Upon ...
Utility ZC's user avatar
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What are the advantages of using partial pivoting in Gaussian elimination compared to rounding off in solving systems of equations?

What's the advantage of using partial pivoting (alternative Gaussian elimination)? In this case, I can use it because if I approximate the result x2 to 1, I'll get strange solutions... But... what's ...
Gjhdby5 Vjfhu's user avatar
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How to derive the relation of a and b according to critical points (including compressibility factor) from Peng Robinson EoS

I've been trying to prove the relation of a and b according to critical points of PR EoS: prove that a and b are: a = 0.457 (R^2T_c^2)/p_c , b=0.0778(RT_c)/p_c I tried to prove it by doing the partial ...
roee danan's user avatar
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Which failure probability is low enough to be considered as 'will not happen'?

Like you will be fired/sued/shot if it happens. I use 1 / 100 million / year (global catastrophes happen on Earth every 100 million years so it is likely no one will care about me) But maybe there is ...
Sergey Alaev's user avatar
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Book claims one can derive USCS mass unit "slug" from temperature equation shown in screen shots below

In the screenshots below, the author claims that one can derive the mass unit "slug" by somehow using the equation shown in the first picture. I understand how could derive a slug if you ...
NO CURE's user avatar
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Ideal axle diameter function derivation

I am interested in the reference of and any papers that discuss the derivation of the "ideal axle". By an ideal axle I mean an axle that has the same strength along all its cross sections. I ...
User198's user avatar
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Which way should angles be measured given a coordinate frame, according to convention?

I am building a 2D Electric unicycle model and have a somewhat trivial question concerning convention when defining a coordinate system. The EUC is constrained to move upon flat ground, and a figure ...
Matthew Ediz Beadman's user avatar
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Unit conversion error - Darcy Radius of Well Influence Equation

I'm having a little trouble. I'm trying to convert the answer from imperial to metric but can't seem to get the answer to match. I am using the formula attached (Darcy Radius of Well Influence ...
Wyatt Sutcliffe's user avatar
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Type of Lyapunov surfaces corresponding to a specific Lyapunov function

Consider the following Lyapunov candidate function: $$ V(x,y,q_i) = \frac{1}{2}x^2 + \frac{1}{2}y^2 + \sum_{i=1}^{n}\ln\big(\cosh(q_{i})\big) \tag1$$ where $q_{i} = \sqrt{(x-x_{i})^2 + (y-y_{i})^2} - ...
Teo Protoulis's user avatar
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Creating a model of an unknown plant/control system

I am getting stuck on the math of control systems. I would like to represent my control system as a differential equation/model. Though many examples use constants which I dont seem to have. I have a ...
Thomas's user avatar
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How to calculate the RPM required from a DC motor in order to pull an object that is attached to wheels

I am attempting to make my first project idea of using a DC motor as a winch motor in order to pull an object, I am using string as the rope to pull object I am attempting to "winch" (air ...
 Aidan Docherty's user avatar
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Static problem with multiple trig terms, one variable

I've encountered an equation that origins from a mechanical static problem containing a spring. I think the simplest formulation is the following: $$ (a- \sqrt{b-c*cos(x)})*cos(d-x) = e*cos(f+x) $$ ...
Johan Dahl's user avatar
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Mathematical descritption of spur gear undercut

I'd like to a plot spur gear in python (using matplotlib, but that is not important..). I've already worked out the involute curves, which can by parametrized easily and which define the main part of ...
mrklMik's user avatar
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1 answer
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Cost/Objective Function Normalization (MPC)

I am trying to develop an MPC. In this MPC, I predict the temperature and try to bring the sensor value to the desired setpoint temperature. I predict the temperature in the next 180 minutes for the ...
Clankk's user avatar
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A transfer function relating jet engine thrust to pitch angle during a phugoid motion

I am doing a school project that requires me to find a transfer function that relates the thrust of a jet engine (which could change with time in one way or another) and the aircraft's pitch angle ...
Faito Dayo's user avatar
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How can we calculate the combined stiffness of a spline connected to a straight member?

I have a geometry that looks something like this. What will be the combined stiffness of the members?
Ahsan Cheema's user avatar
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What are the change in forces with a ribbon under tension is twisted?

Consider pallet strapping. It has width W. When the strap is flat, it has some maximum breaking strength B. Now, let's put one twist in it over X feet. Mentally we have a VERY skinny isoceles ...
Sherwood Botsford's user avatar
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1 answer
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Kinematic description of a gear rack moving around a cogwheel

I am facing some issues regarding the kinematic description of a gear mechanism (or maybe more accurately gear manufacturing process). Basically I would like to obtain an animation, where the cogwheel ...
Richard's user avatar
1 vote
2 answers
359 views

What is the moment of inertia of a circular segment?

Hi I read this response but it isn't exactly my situation I have a circle where the axis of rotation is on the c axis like this for a segment equal to the green. Specifically, I have a round steel ...
Simon Boucher's user avatar
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Iterative Method through FEM

Due to reasons, I can not fully describe the process explicitly so I will be using substitutes to represent the variables. Nomenclature: x - an independent variable y - another independent variable Fz ...
lone_coder's user avatar
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1 answer
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Factoring Quadratic Equations

Given a general polynomial of the form ax^2 + bx + c = 0, we can factor it to be the product of two terms eg. (x+d)*(x-e) = 0. Why is it that we can use substitute BOTH equations as equalling zero? If ...
cav3's user avatar
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Drone Geometrical Shape

Drone Can Drones be designed with geometrical shapes viz Kite, Cylinder, Sphere etc?
Prashant Akerkar's user avatar
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Genetic algorithm implementation for gas/power/water network operation optimizaiton

I have both practical and theoretical background in power, gas and water networks operation and I am familiar with the basics of genetic algorithm. I would like to dive into the network operation ...
artp9's user avatar
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1 answer
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How to model a driver's appropriate braking for deceleration, and throttle for acceleration for a car moving on a straight road?

A project team within my company is stuck on a conundrum and have asked me for some insights. They want to develop a driver model (mathematical or drawn) where input is the car's velocity profile, and ...
Balaji Harihar's user avatar
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2 answers
467 views

Second moment of area (moment of inertia) for annulus segment

I am a Mechanical Engineering student and I'm working on some calculations for an assignment at a company. As a part of this assignment I need to calculate the moment of inertia (Ixx) of a segment of ...
Lars's user avatar
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How to solve this thermal equilibrium

I was studying and came across a problem that I'm not sure how to solve. In fact, I think it gives me 1 degree of freedom. In the problem, I am asked to calculate the time and temperature required to ...
darth momin's user avatar
1 vote
1 answer
65 views

Matrix Calculation

I would like to Calculate Q. The transpose of U matrix is a 2x5 matrix and U is a 5x2 matrix. Therefore, I was expecting a 5*5 Matrix, which wasn't the case. Can someone please help me to solve Q ...
Rayleigh's user avatar
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How to re-write systems of two linear second order ODEs in a state space form

I have recently been working on how to convert ODES into state space form, and I came across this problem that has me confused. Should B in the state space be [1; -2] or [1 0; 0 -2]? I think the ...
Ray's user avatar
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Why is the vector cross product different here?

I was taught that the linear velocity of a body rotating around a fixed axis is the cross product between the angular velocity and the position vector. The vector for the velocity here in this picture ...
S.M's user avatar
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Calculating forces on cables

I have to calculate the pull forces of Fab and Fac. I have used extended Pythagoras to find the length of AC and AB but I have no idea how to calculate the forces. I also tried to use cartesian ...
daan 's user avatar
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1 answer
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Rotation of point in 3D space

I want to rotate a point (3,4,5) by an angle 45 degrees(0.785398 rad) in 3D space. I have used the standard DCM matrix in the order Rx, Ry and Rz. Where, $\theta = 0.785398 [rad]$ $$ Rx= \begin{...
Tanvi Sawant's user avatar
1 vote
2 answers
350 views

Clock pendulum period vs driving weight

I've got a weight-driven pendulum clock, I increased the driving weight by 10% and the period decreased by 1%. Why? What's the equation? The pendulum is length = 32cm; bob weight = 7g; rod weight = 7g....
Peter Balch's user avatar
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1 answer
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Rotation of Radar Axis in 3D plane

I'm working on a sensor fusion application. In our vehicle, 4 radars (fixed, non-rotating radars) are placed at 4 corners of the vehicles at 45 degrees with respect to x, y and z-axes of the vehicle. ...
Akash Sagar's user avatar
-2 votes
1 answer
148 views

How to convert PI controller in to differential equation?

I want to convert PI controller into Differential Equation form. How should I do this? Please help me.
aman2909's user avatar
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36 views

Operations between rotating elements

Given two (or more) rotating elements, which mathematical operations can be done between them? For example: Different gear ratios can be used to multiply a rotating element's angular velocity by a ...
impresso's user avatar
2 votes
1 answer
98 views

How to solve for discrete state space matrices given input and output

I have a set of time-series data that consists of inputs $u_k$ where $ u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this ...
ian.cooke's user avatar
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59 views

How do I find the optimal position for a hydraulic damper to balance the force applied to a rotating assembly?

This may be a simple problem, my math and physics chops are a bit rusty. I'm modifying a flight sim rudder pedal to add a hydraulic linear damper (specifically a motorcycle steering damper). I'm ...
Tyler Doe's user avatar
1 vote
2 answers
1k views

Is the maximum bending moment of a fixed end beam always at end?

Mathematically, we can see that with downward loads only (only upward loads at the ends), the maximum bending moment for a fixed end beam of span $L$ either occurs at $x=0$, $x=L$, or where the shear ...
JP McCarthy's user avatar
1 vote
1 answer
71 views

How do I find a target standard deviation for my own testing given a confidence level, a mean, and bounds for the interval?

I'm working on a project involving a couple of material dispensers, and the customer we're designing them for has asked us to keep the output of the dispensers within a set range 95% of the time. I'm ...
Grumpy's user avatar
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How do you derive the formula for converting weight percent to atom percent?

I have the following equations for weight and atom percent: Where m is the mass of each element. where A is the atomic weight of each element and m prime is the mass of each element. And I'm told ...
George Young's user avatar
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1 answer
82 views

Euler-Bernouilli for a beam with force in the middle

A beam of length $L$ is held a $x = 0, L$. A force $F$ in the middle ($x = L/2$) pushes the beam. The Euler-Bernoulli equation can be written as such: $EI\frac{\partial^4 y(x)}{\partial x^4} = F\delta(...
mooder's user avatar
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1 answer
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What would the dynamics and measurement operators be in this control theory problem/code, and where can I generate them from?

I'm working on something slightly outside of my scope of work, and I can't figure out if I fully understand what these things mean. Could someone help explain what the dynamics operator and ...
Applesauce44's user avatar
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0 answers
69 views

How to calculate velocity east, north up having lat/lng/alt/time?

I have a certain values from a camera and wondering how the velocity east, north and up is calculated. Here are the values ...
code0x00's user avatar
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1 answer
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What is percent of thread depth when it comes to screws?

What, geometrically, is meant by percent thread depth? And, what would constitute 100% thread depth? I have been trying to derive the equation for thread percentage in the textbook Machine Tool ...
skale's user avatar
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2 answers
199 views

Maximum Deflection for simply supported beam under arbitrary triangular loading

I am trying to get the: maximum deflection location of maximum deflection deflection at any point For a beam under an arbitrary triangular load (i.e. a, b, c, and w can vary). I tried to solve this ...
StringTypeGroup's user avatar
1 vote
3 answers
158 views

Use of 'parameter' in engineering?

Is there a different meaning to the word of 'parameter' in engineering? I've started in engineering from a mathematics/physics background, and commonly a 'parameter' is either used to 'parameterize' a ...
user1007028's user avatar
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1 answer
256 views

Timoshenko Fixed Fixed Total Beam Deflection

I am trying to solve a problem where there is a fixed-fixed (clamped-clamped) beam with a point load in the middle (at L/2). The L/H is less then the 10 required for normal beam bending analysis and ...
3BeaversInATrenchCoat's user avatar
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2 answers
137 views

Why $\frac{m}{V}$ gives average density when density varies?

This might be a very basic question, and for years I have gone by simply accepting it as a fact. That whenever the density is uniform the formula $\frac{m}{V}$ gives that uniform value of density and ...
Harshit Rajput's user avatar
1 vote
3 answers
90 views

Why stopping at the first derivative in conservation equations?

Oftentimes we, as engineers, have to write energy/mass/momentum balances to derive the governing equations for a quantity $\phi(x,t)$ of a physical system. One of many derivations of such balances ...
TheVal's user avatar
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