Okay, got it. Thank you! But maybe a follow-up question: that doesn't mean my other computation with the tangent projection is wrong ?
Is my other formulation with the tangent projection also correct, but a little more complicated?
in the upper example there is no curvature. in the bowl system the contact surface has a curvature. this means in the 2 drawn examples that the frictional force acts in different directions. so the magnitude in y direction for example is in the left example bigger then in the right example. when...
That doesn't make sense. what you describe is only valid if the contact pair has no curvature! What you describe are the following equations:
$$
F_x^{\text{friction}} = -\mu \cdot \lambda \cdot \text{sgn}(\dot{x}_{\text{rel}})
$$
$$
F_y^{\text{friction}} = -\mu \cdot \lambda \cdot...
okay I see, but let's say I leave away the tangent projection and just use:
$$
F_x^{\text{friction}} = -\mu \cdot \lambda \cdot \frac{\dot{x}_{\text{rel}}}{\sqrt{\dot{x}_{\text{rel}}^2 + \dot{y}_{\text{rel}}^2}}
$$
$$
F_y^{\text{friction}} = -\mu \cdot \lambda \cdot...
okay is this then correct
The friction forces in the tangential direction are modeled as:
$$
F_x^{\text{friction}} = -\mu \cdot \lambda \cdot \hat{T}_x \cdot \text{sgn}(\dot{x}_{\text{rel}})
$$
$$
F_y^{\text{friction}} = -\mu \cdot \lambda \cdot \hat{T}_y \cdot \text{sgn}(\dot{y}_{\text{rel}})...
yes, the bowl accelerates and has different velocities.
the ball is modeled as a pointmass and is therefore only sliding.
Okay I'll try to rephrase this. In my model the ball is described in cartesian coordinates. So it has a acceleration in x and y. Therefore I have two differential...
Here I need to model the Frictional force in cartesian coordinates. I already set up the lagrangian and derived the expression for the normalforce. But the Friction in the lagrangian appears on the right hand side of the equation in the non conservative force vector. So I have to set up this...
Yes, I agree. When the ball is in contact with the bowl they share the same normal velocity. Therefore the relative velocity should be parallel. I set up the dynamics equations of the ball in cartesian coordinates in x and y direction. And coulomb friction is not dependent on the relative...
Consider a 2D circular bowl with a point mass moving inside, as shown in the picture. Assume that the normal force N acting on the mass is already known and keeps the mass constrained to the curved surface of the bowl.
I want to model Coulomb friction in this system so that, for example, if I...
Okay so here is the Problem Statement:
A 2-dimensional circular half-bowl of mass M and radius r is shown in the figure. Inside the bowl lies a point mass m that can move frictionlessly along the inner surface of the bowl.
The bowl is free to move translationally in the xy-plane, but it cannot...
Yes, your guess is basically correct. If it's easier for you to see it as a pendulum thats also fine. But this is only valid if the the y coordinate is smaller then 0. Otherwise the ball leaves the bowl and should be in freefall. Because of this I think it's better to stay with the bowl. I also...
ah okay, but then it makes no sense for my problem because the acceleration is not constant as it is my controlinput of the system.
yes you can put it like this (b). I want to find x(t) and y(t) when the bowl accelerates. So I need to know how the acceleration of the bowl affects the ball, by...
okay I can try but I'm not sure if I'm able to rotate to cartesian coordinates. Maybe I need some help there. I'm going to derive the equations and share them :)
I'm trying to find a function in matlab for an ODE-solver
so the function looks like this:
function [dYdt, N, theta] = fcn_pointmass_in_movable_bowl_cart(~, Y, r, g, u)
% Unpack state variables
x = Y(1); % Bowl center in x
y = Y(2); % Bowl center in y
x_c =...