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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Modelling a Simple Translational System

I posted this on stack exchange physics, sadly no one has answered so I thought I'd try my luck here. I am trying to model the following translational mechanical system in I/O form, however I am ...
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Relationship between the infinity norm of estimation error and the trace of estimation error covariance matrix in Kalman filter

I am working on designing an interconnected distributed control system. In this system, I need to use Kalman filter because the measurements are noisy. I have two questions: 1 - What is the ...
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Rigid-flexible multibody dynamic coupling terms

Suppose a multibody consisting a rigid and a flexible parts. When the rotation dynamic of the rigid and flexible part are derived, we see angular acceleration of rigid part, $\ddot{\theta}$ in ...
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Is this kind of steering possible?

I would like to build a small robot and was wondering if a particular configuration of steering would even be possible and stable. What I would like is to have the two rigid axles mounted on a ...
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1answer
40 views

Peristaltic pump - theory vs reality, where is a problem?

I'm building a test system (experiment) for peristaltic pump to check if pump is able to pump according to specification. The pump data: 6,3ul liquid moved per stroke. 5 strokes per revolution. The ...
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48 views

How does one deal with indeterminacy in modeling the motion of vehicles with multiple wheels? (Dynamics Question)

Consider a vehicle with four wheels and suspension (coil and dampers) rolling over an arbitrary surface. What would be the magnitude (not direction) of the normal force on each wheel? Is there a ...
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34 views

Easy software for : Multibody dynamics of rigid bodies?

I am currently searching for an easy-to-use tool to understand/simulate multibody dynamics of rigid bodys. I have no engineering or mechanics background (I am from IT) and I feel that I cannot imagine ...
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34 views

Time Constant For Step Response First Order System

I ran several experiments where I attached my phone to a motor and collected the angular velocity at different step inputs( different voltage values). My question is, is it possible for the motors to ...
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Torque Required From Motor For a Project

The device I am building is responsible for supporting 200 lbs and is required to accelerate 10 feet per second. The device will have two 8 inch diameter wheels. I have worked out what I believe to be ...
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1answer
30 views

Modeling the Internal Forces Exerted on a Catapult Arm while Throwing

I am currently creating a MATLAB script to determine the internal forces present in a uniform beam as it is accelerated by a torsional spring. I was able to derive the equation for the axial force ...
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37 views

Control System Response

How does one find the zeta value or the frequency of an over damped response curve. I am used to determining things by using the log-decrement equation. Does that apply here even though there is no ...
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92 views

Is there a simple trigonometric relationship between these two angles?

The setup shows 3 rigid links (with fixed lengths) constrained by 4 joints. The blue joints are fixed in place and only allow rotation, while the black joints can move and also allow rotation. ...
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How can you make a solid box jump up with no external forces?

Let's say I have a box lying on a flat surface. Inside the box, I make a heavy mass hang from a spring attached to the top of the box. If we pull the mass all the way down and let it go, I believe it ...
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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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61 views

Rover Steering Torque

I would like to calculate the required motor torque to turn a rover wheel whilst the rover is stationary. I have modelled the friction force as a distributed force acting equally along the width of ...
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2answers
74 views

How long does it take and how far does it travel a sphere in free fall before reaching a percentage of the terminal velocity?

Assume a sphere (hail) that is free dropping in air. At some the sphere will reach close to the terminal velocity. The question is: how long $t_p$ in seconds does it take before a percentage $p$ of ...
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1answer
44 views

Does the terminal velocity of a sphere in free drop increase with increasing diameter?

I was trying today to calculate the terminal velocity of a hailstones with increasing diameter and mass. I was trying to figure out if larger hailstones will have a higher impact velocity or lower. I ...
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80 views

A question on resonance

This is to settle a debate. I was working on a scaffold next to a building, as the wind blew, the scaffolding would sway. As I stood there I was trying to maintain my stability, but my movements ...
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66 views

Question about a Force in FBD of a garage door

I am not sure how to draw a certain force in a FBD (Free Body Diagram) of a garage door. The Garage door is indicated by B-C (2m height) in the picture below. If this door is closing, how should the ...
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33 views

How is rack and pinion steering configured for different wheel/axle spacing?

The rack and pinion is supposed to turn each of the front wheels differently, such that lines orthogonal to the wheels will intersect in line with the rear axle: Which components of the rack and ...
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1answer
59 views

Why is the sum of binormal forces equal to zero?

I've read in Hibbeler Dynamics, page 131, that when considering a coordinate system with normal and tangential axes, the sum of binormal forces equals zero. I don't understand why this is true, maybe ...
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1answer
181 views

Modeling rigid body dynamics: Trouble with equations, encountering nonsense answers

Hi, I am working on modeling a simple rigid body dynamic system through a certain range of motion. Here is the picture of the system. I am trying to solve the system for the variables $x_1'', y_1'', ...
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26 views

Plane Wave Expansion method

I have very recently ventured into the domain of periodic structures. In the literature, I came across the Plane Wave Expansion method to compute the dispersion curves. I managed to code it in 1D . ...
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1answer
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
107 views

Free body diagram of a differential-drive mobile robot

I'm trying to study the free body diagram of this differential-drive mobile robot in case of straight trajectory (same torque applied on both of rear wheels) and pure rolling motion I started ...
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2answers
112 views

is a positive acceleration indication that velocity must be positive?

the question is clear and straight forward but when i get the velocity it should be ±√2 what i don't understand is the guide answer refusing the -ve value because acc is always +ve thank you in ...
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1answer
59 views

Determine the minimum horizontal force to disturb the equilibrium

Three blocks of 1N 2N and 3N are placed one over the other respectively. If the friction between the topmost 1N and the middle 2N block is twice the friction between the lowest 3N and floor then ...
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Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle

My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
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47 views

How to get the normal acceleration

For the problem below, I tried solving it, but I don't know where I should get the value of normal acceleration, guess I was lost. And here's what I solved so far
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1answer
93 views

Why does my trimmer feels heavier when it is operating and its fully charged?

I have a Philips trimmer which when fully charged feels much heavier than when it is not charged. Also , the blades move much faster when it is fully charged I.e it’s weight , speed of blades kind of ...
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1answer
51 views

Input signal rescaling block [closed]

The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown. The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
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62 views

Find a constraint relation for this Q of 3 pulleys and 2 blocks attached with string

Using any method find the constraint relation between mass 1 and mass 2. Assumptions: No friction , massless string and pulley. Q: Find constraint relation between 1kg and 2kg block. what I tried so ...
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62 views

How do engineers reduce vibration of system with multiple known natural frequencies? How do they design the isolation system for specific frequencies?

I have a system that is pretty much a chamber that needs to sit on the ground. I measured the transmissibility of the chamber vs the ground (output/chamber acceleration over input/ground acceleration) ...
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48 views

Trajectory of the center of mass of a vehicle

The problem is to find the trajectory of the center of mass of a car when it is rotating and translating (after an off center collision, for instance) What i know as input is the trajectory of the ...
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34 views

Conceptual question about rotational and translational kinetic energy

My real life problem is to calculate initial translational and angular velocities of a vehicle in a loss of control to a stop. (The vehicle will translate and rotate about it's center of mass.) ...
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47 views

Are equilibrium values of a differential equation uniquely dependent on its constants?

I have a dynamic model which undergoes two distinct stages. The system starts out with certain initial conditions and once a specific point is reached in stage 1, these ending conditions are used as ...
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48 views

Velocity and Acceleration Polygons for Mechanism

I need to determine the velocity and acceleration of point H using vector equations and drawing a polygon. Given data is shown. $\omega$2 is 5.8 rad/s and $\phi$2 is 120 degrees I know how I can draw ...
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2answers
381 views

Reaction force at a pin joint for a rod that is rotating about a fixed axis

In this diagram, assuming there is no friction between the pin joint and the rod, I understand that the rod will rotate about $O$. However, let's say that the rod is released from $ \theta = 0$ and ...
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1answer
39 views

Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance

Suppose a system is described by the following ODE: $$\dot{x} = f(t,x)+u$$ where $x$ denotes the state of the system $f(x,t)$ is an unknown nonlinear function which meets the following condition: $$ ...
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Find orientation of reference nodes in Abaqus

I am constructing a simplified model of a pontoon-supported floating bridge in Abaqus. I have chosen to represent the pontoons as one-noded user-elements defined from the mass and stiffness matrix for ...
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90 views

Angular acceleration of the CD bar

Determine the angular acceleration of the $CD$ bar for the situation illustrated in the figure. The solution is $474 rad/s^2$ $counterclockwise$ I've done: $v_B = v_A + w *r_{AB} <=> v_B= -3j$ ...
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2answers
68 views

Fault Recovery of a UAV using MATLAB

I'm currently investigating fault recovery in a UAV using MATLAB. I've been given several variables: phi = the roll angle psi = the yaw/heading angle beta = the side slip p = roll rate r = yaw/...
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1answer
54 views

Proof of angular velocity identity

I've been going thru the book by Hodges and Roithmayr regarding dynamics theory and I can't seem to prove that: I have tried using multiple substitutions, including the fact that every component of ...
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1answer
36 views

why do we need state feedback in H-infinity concept instead of output feedback

I have faced control of a flexible manipulator which have a zero dynamic related to flexible parts dynamic. the zero dynamic states (generalized states) are not observable in input-output dynamic and ...
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1answer
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Linearisation of the Equations of Motion of an Inverted Double Pendulum

I am working to develop a deep reinforcement learning model for balancing an inverted double pendulum. To do so, I needed to derive the equations of motion, via the Euler-Lagrange (EL) method and now ...
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1answer
48 views

Pulley with mass dynamics question

A pulley system has mass moment of inertia of 1.4kgm^2. If 8kg block is released from rest from S=1, by using energy approach what is angular velocity at S=2? Radius of pulley is 250mm. Note S is from ...
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43 views

Angular Acceleration

Need confirmation for this question please: A pulley with Radius of 90mm and a mass moment of inertia 0.28$kgm^2$ about its central axis is subjected to a torque of 50Nm about this axis. What is ...
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48 views

Condition for equilibrium of a rigid body on a horizontal surface

The following question is from a past paper from Further Mechanics and it has been bothering me immensely I have spent hours cracking at a way to make sense of it, the question is in two parts Part ...
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66 views

Mechanics Dynamics Question

Alright so this is my question lasses and lads: a disc with a mass moment of inertia 0.125kgm^2 about its central axis is rotating at 180rad/s about the axis. What is the angular momentum of the disc ...
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Sprocket Angular Velocity [duplicate]

I have a question please that I need help on. Consider the chain that is draped over the sprocket with mass moment of inertia of 0.005kgm^2 about central axis. If 4kg block is released from rest from ...

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