Questions tagged [dynamics]

Questions about the dynamics of a system. Currently there is a very large scope ranging from from dynamics in mechanics, vehicle and flight dynamics, to system dynamics and fluid dynamics.

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18 views

Gear/Mechanics problem: How to design to allow for 2 types of rotation

I am designing a new mowing system that can effectively mow around poles. The machine consists of an arm that is attached to the back of a tractor and runs off its PTO. At the end of the arm is a ...
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23 views

How to find angle using Torque-Inertia [closed]

I want to find angle(radians) using the formula: τ = Iα . I guess after finding angular acceleration α I have to do an integration but I am not sure which method I should use. Thanks
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29 views

Is the relative acceleration with respect to a translating frame equal to that with respect to a fixed one?

My book, written by Beer, states that the rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in translation. But while it says the derivative ˙rB/A ...
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correcting mode shape for modal damping

I have mode shapes and eigen frequencies from FE simulation. I have modal matrix and eigen frequencies corresponding to each mode. The mode shape is mass normalized. I am required to correct each ...
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Modal analysis in Abaqus AMS solver

I have a huge model for which I am performing modal analysis. Abaqus fails to solve with Lanczos solver and hence I use AMS solver, which successfully computes the solution. But since AMS solver ...
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29 views

How do I determine the angular acceleration?

In this question I understand what we have to do to solve it and is equate the sum of moments with the moment of inertia. However I am not sure on how the LHS became negative as I see that the angular ...
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37 views

Quantifying the reaction force on fixed tubing connected to a peristaltic pump

I am not sure how I should consider the forces due to hydrostatic pressure when calculating the reaction force due to a fluid being pumped through fixed tubing with a peristaltic pump that I am using ...
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36 views

Find frictional losses as box exits ramp

I have a box traveling on a ramp just before the ramp levels out. At this point all values are known: I want to calculate the frictional losses from this point to when the box is completely off the ...
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52 views

Changing the quality of the transient process in a nonlinear system (Part II)

My question is a continuation of the topic. https://math.stackexchange.com/questions/3910814/changing-the-quality-of-the-transient-process-in-a-nonlinear-system-in-mathemat Unfortunately, last time I ...
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80 views

Why does the frequency of a bottle filling up changes?

Today as I was filling up a bottle of water, and I could hear the distinctive change in pitch that signals that the bottle is near filling up, I started wondering what equation determines the ...
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77 views

Determining Friction and Contact forces

I am looking at a rod that has an acting force along one end that's pinned into a frictionless track. The other end is pinned into a track that has friction. I am trying to determine the contact ...
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62 views

How to determine the linear and angular velocity of one end of a rod that is pinned on a track on each side?

I am working on trying to determine the velocity of one end of a rod that is pinned on both ends into two different tracks. One track is linear and the pinned end has known values. The other side is ...
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Changing the quality of the transient process in a nonlinear system (in Mathematica)

I urgently need advice and help. I have a system of differential equations like this: $\begin{cases} \frac{dx}{dt} = y[t] \cdot \alpha \cdot sin(\omega t) + \frac{d}{dt}(\alpha \cdot sin(\omega t)) ...
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38 views

Coulomb damping time calculation

I'm designing a movable cover on rails under a spring and with added friction to dampen the movement. The model that describes it's movement the best is Coulomb damping model. The cover is moved from ...
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46 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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129 views

What is the maximum force needed to move the roller block from point A to point B and where does that maximum force occur?

Hello everyone. This project is for a very specific application and I am trying to determine the force necessary to get the block from point A to B. Specifically the maximum force necessary and at ...
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39 views

Estimation of Beam Displacement from Acceleration

Hi Engineering Exchange, I have a beam with pinned-pinned boundary conditions (free to rotate but not free to translate). A legacy computer analysis provided me with the maximum mid-span acceleration ...
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41 views

Research of transients in nonlinear systems with linear dynamic links

I am having difficulties of this nature. There is a nonlinear system of the following type: I need to analyze analytically the transient process in such a system. The analytical study of the ...
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98 views

Disc Brakes - Swept Area , why is larger better?

I am trying to understand why a bigger swept area on disc brakes provides higher braking force for the same force being exerted on the brake lever/pedal by the rider. If we use the same exact brake ...
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1answer
20 views

At what volume would air bubbles become static in a fluid with viscosity of 7000cps

I would appreciate any help with this as its been a few years since my fluid dynamics courses at University! Basically I am trying to determine the cause of voids that we are seeing in a set resin. ...
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28 views

Triggering of eigenmodes

When conducting an eigenmode analysis, we get a sequence of different modes with their respective eigenfrequencies. My question is: Are all of those really relevant in every application? Take for a ...
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36 views

Force on suspension when hitting a step

I'm trying to calculate the magnitude and direction of the force exerted on a wheel when encountering a step. The wheel and the steps are non-deformable. I found two different approaches: energy ...
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3answers
91 views

Difference between Linear Force and Force about an Axis

I am confused between How forces work when applied in singular linear direction vs Force Applied to a continuous mass about an axis(example to rotate it). Example 1: Consider an object of mass $m$ ...
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Kinetic energy of a rigid body

A homogeneous disk with radius $R$ and mass $m$ rolls without sliding on a horizontal fixed plane. Peripheral point $A$ has velocity $v$. Determine the kinetic force of the disk. In my textbook they ...
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Skew-Symmetric Gain Matrix to Encourage Exploration

I am reading a paper on controls and it has the following snippet: We propose to use the control law $$u_i = K(CV_i − p_i)$$ , where K is a (potentially time-varying) uniformly positive definite ...
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Moment equation from dynamics differs with equations from physics & statics. Where did I go wrong?

In my dynamics class, we're being asked to solve the following problem: My Attempt: Since I'm given the initial velocity, final velocity, and distance, I solved for the acceleration of the plane ...
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25 views

Deformation and stress in moment of hit (Ansys)

This how task goes: i need to find deformation and stress of piston in moment of hit between piston and tool (tool is stationary). Velocity of a piston is (5-7 m/s) and forces are in picture below. I ...
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55 views

Equation governing relative motion between aircraft and store

I am reading a paper titled Conditions for safe separation of external stores by EE Covert [Link]. In Section 1 Introduction of the paper, the author has given an expression for $d$, the relative ...
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3answers
33 views

How to solve a system of second order ODE from time t = T to t = 0

I have a system of second-order ODEs $$ \mathbf{M\ddot{x} + C\dot{x} + Kx = f} $$ I want to know some good numerical methods to solve this system of the equation given the initial conditions at time $...
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55 views

Unit Conversion for Mass Density

I am doing a Finite Element analysis of a continuum. In my problem definition I use these units: mm for length, kPa for applied stress, and MPa for material stifness (Young's modulus). With these ...
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23 views

What is the best way to find solved problems similar to the one at hand?

This is a general question, so sorry if it breaks the rules. However, I think it is very important as more often than not someone else has already solved a similar problem that can be applied to solve ...
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1answer
23 views

Dynamics - Deriving Linear acceleration based on angle theta

Suppose that I am given an equation of some positional vector in the Cartesian coordinate system that is based on some theta shown right below. I am asked to find the linear acceleration based on ...
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40 views

How to Calculate Torque to Prevent Rotating

I'm stuck with how to calculate the external torque which must be applied to prevent the aircraft rotating about axis? The imagine shows an aircraft which has a jet engine with a rotor that has an ...
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43 views

How to calculate the polar mass moment of inertia

Recently ran into the polar mass moment of inertia when calculating the gyroscopic moments of a rotating shaft. However I hardly find any information about this quantity. Can anyone help me how to ...
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1answer
26 views

What is the relationship between Rotational speed (RPM) and the speed of a drone (Air speed)

I would like to know whats the relationship between these two, is it linear? or what? also i would like to know the mathematical relationship between these two. Thank you
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1answer
43 views

Does the surface roughness play any role in shock absorbing?

Consider a mass of about $130 \pm 10 $ kg, falls from height, let say $2.5 $ m. In order to dampen the vibration and sound, I use silencer or drop pads. I was wondering if introducing the macroscopic ...
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196 views

Stopping force on wire rope from a falling object

Okay, bit of a weird one. Imagine an object of known mass in free fall, tethered by a wire rope to an infinitely stiff sky hook. When that wire rope eventually tightens, what will be the stopping ...
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30 views

Elastic waves in very thin plate

Elastic waves in structural elements are described by \begin{align} \rho \frac{\partial^2 u}{\partial t^2} &= (2 \mu + \lambda) \frac{\partial^2 u}{\partial x^2} + \mu \left( \frac{\partial^2 ...
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1answer
266 views

Calculate max deceleration without front wheel slipping (bicycle)

I am trying to calculate the maximum braking force/deceleration for a bicycle. Note: the question assumes only the front brake is used Free body diagram: For dry tarmac where I know there is enough ...
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2answers
35 views

Position vector to Velocity vector

Is it possible to derive velocity vector form position vector without unknown such as: position vector of A = (0.8)i + (1.2)j?
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46 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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70 views

The optical encoder resolution

The optical encoder has a code wheel with a single track of slots and two photodetectors. The photodetectors are positioned so that they produce signals with a 90 degree phase difference. I want to ...
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1answer
205 views

Motor, a gearbox and a drum with a cable lifting a mass

A lifting device consists of an electric motor, a gearbox and a drum with a cable for lifting a mass. The speed after the initial acceleration is $v=0.5\,\text{m/s}$. The gear efficiency $\eta=0.7$ ...
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1answer
53 views

Moment of Inertia

To calculate the moment of inertia at o, I tried to apply (1/3mq^2) but I am not sure if it is correct. Any help would be appreciated.
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76 views

Inertial Forces while analysing forces on a Piston in a Slider - Crank Mechanism?

I get that we are analysing the Piston in a non-inertial frame of reference, but the point of my question is that according to D'Alembert's Principle, whenever an inertial force comes in the line of ...
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1answer
63 views

Ball and Socket Wheel Concept

I am sure you all remember those prehistoric computer mouses that had a ball under it. I'm looking for any points and tips on how to create a ball and socket wheel that has an almost frictionless ...
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2answers
74 views

How to calculate traction force w.r.t. rotational speed of a shaft mounted at a certain angle on a surface?

I am designing a new mobile robot platform and i need a generic solution for the robot in order to establish a proper mathematical modeling. My question is about calculation of the traction force of ...
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1answer
22 views

How can I validate the validity of a model of a dynamical system?

I derived a non linear differential equation system for a mechanical system. However I doubt the correctness of it. So I compared the model's dynamics with a VREP simulation. I did this by by Euler ...
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38 views

Approaches to whether a projectile gets intercepted

Hi everyone, How do I approach questions like part (ii)? From what I understand now, I believe the shortest method is that as long as the ANGLE of the relative velocity of B with respect to velocity ...
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57 views

Would a plane lift from ground if in a free treadmill?

I was wondering if the force generated from the engines of a jet plane would lift it up from the ground if in a free treadmill. Would it take off?