D2. Interaction forces between particles - Revision history

Eantem: /* D2.8 Friction */

2026-02-17T11:31:29Z

D2.8 Friction

← Older revision		Revision as of 11:31, 17 February 2026
Line 310:		Line 310:
	When particle '''P''' moves relative to the rough surface of the rigid body S, the tangential force is not a constraint force but a friction force, and always opposes the speed of '''P''' relative to S:		When particle '''P''' moves relative to the rough surface of the rigid body S, the tangential force is not a constraint force but a friction force, and always opposes the speed of '''P''' relative to S:

	<math>\vec{\Fs}_{\Ss\rightarrow\Ps}^\text{friction} = \|\vec{\Fs}_{\Ss\rightarrow\Ps}^\text{friction}\|\frac{\vel{P}{S}}{\|\vel{P}{S}\|}</math>		<math>\vec{\Fs}_{\mathrm{S}\rightarrow\Ps}^\text{friction} = -\|\vec{\Fs}_{\mathrm{S}\rightarrow\Ps}^\text{friction}\|\frac{\vel{P}{S}}{\|\vel{P}{S}\|}</math>

	There are several models for formulating the value of <math>\vec{\Fs}_{\Ss\rightarrow\Ps}^\text{friction}</math>, depending on the characteristics of the contact between '''P''' and S.		There are several models for formulating the value of <math>\vec{\Fs}_{\Ss\rightarrow\Ps}^\text{friction}</math>, depending on the characteristics of the contact between '''P''' and S.

Bros: /* ✏️ Exemple D2.1: gravitational attraction between two satellites */

2024-11-11T19:53:39Z

✏️ Exemple D2.1: gravitational attraction between two satellites

← Older revision		Revision as of 19:53, 11 November 2024
Line 161:		Line 161:


	====✏️ ~~Exemple~~ D2.1: gravitational attraction between two satellites ====		====✏️ Example D2.1: gravitational attraction between two satellites ====
	---------		---------

Bros: /* ✏️ Exemple D2.2: attraction force of a spring with linear behaviour */

2024-11-11T19:53:23Z

✏️ Exemple D2.2: attraction force of a spring with linear behaviour

← Older revision		Revision as of 19:53, 11 November 2024
Line 198:		Line 198:


	====✏️ ~~Exemple~~ D2.2: attraction force of a spring with linear behaviour ====		====✏️ Example D2.2: attraction force of a spring with linear behaviour ====
	---------		---------
	<small>		<small>

Bros: /* ✏️ Exemple D2.3: repulsive force of a damper with linear behaviour */

2024-11-11T19:52:55Z

✏️ Exemple D2.3: repulsive force of a damper with linear behaviour

← Older revision		Revision as of 19:52, 11 November 2024
Line 227:		Line 227:


	====✏️ ~~Exemple~~ D2.3: repulsive force of a damper with linear behaviour ====		====✏️ Example D2.3: repulsive force of a damper with linear behaviour ====
	---------		---------
	<small>		<small>

Bros: /* ✏️ Exemple D2.3: repulsive force of a damper with linear behaviour */

2024-11-11T19:52:40Z

✏️ Exemple D2.3: repulsive force of a damper with linear behaviour

← Older revision		Revision as of 19:52, 11 November 2024
Line 231:		Line 231:
	<small>		<small>
	[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]		[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]
	:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Interaction forces between particles#✏️ ~~Exemple~~ D2.2: ~~força d’atracció d’una molla de comportament lineal~~\|'''~~l’exemple~~ D2.2''']]</span> through differentiation:<br>		:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Interaction forces between particles#✏️ Example D2.2: attraction force of a spring with linear behaviour\|'''Example D2.2''']]</span> through differentiation:<br>

Bros: /* ✏️ Exemple D2.3: repulsive force of a damper with linear behaviour */

2024-11-11T19:48:48Z

✏️ Exemple D2.3: repulsive force of a damper with linear behaviour

← Older revision		Revision as of 19:48, 11 November 2024
Line 231:		Line 231:
	<small>		<small>
	[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]		[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]
	:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Interaction forces between particles#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> ~~per derivació~~:<br>		:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Interaction forces between particles#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> through differentiation:<br>

Apons at 09:02, 9 November 2024

2024-11-09T09:02:33Z

Show changes

Bros: /* D2.5 Interaction through dampers */

2024-11-08T19:58:32Z

D2.5 Interaction through dampers

← Older revision		Revision as of 19:58, 8 November 2024
Line 208:		Line 208:
	<small>		<small>
	[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]		[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]
	:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. ~~Forces d’interacció entre partícules~~#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> per derivació:<br>		:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Interaction forces between particles#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> per derivació:<br>

Bros: /* D2.5 Interaction through dampers */

2024-11-08T18:26:34Z

D2.5 Interaction through dampers

← Older revision		Revision as of 18:26, 8 November 2024
Line 208:		Line 208:
	<small>		<small>
	[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]		[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]
	:~~La força de repulsió de l’amortidor s’obté a partir de l’allargament calculat a~~ <span style="text-decoration: underline;"> [[D2. Forces d’interacció entre partícules#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> per derivació:<br>		:The repulsion force of the damper is obtained from the elongation calculated in <span style="text-decoration: underline;"> [[D2. Forces d’interacció entre partícules#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> per derivació:<br>

Bros: /* D2.5 Interaction through dampers */

2024-11-08T18:23:33Z

D2.5 Interaction through dampers

← Older revision		Revision as of 18:23, 8 November 2024
Line 194:		Line 194:

	==D2.5 Interaction through dampers==		==D2.5 Interaction through dampers==

			Linear dampers introduce attractive or repulsive forces between their ends depending on their deformation rate <math>\dot{\rho}</math>. When the ends of the damper separate, the force is attractive; when they approach, it is repulsive. Unlike springs, dampers do not exert any force between their ends in static situations.<br>

			The force associated with linear dampers with linear behaviour is proportional to that speed <math>\dot{\rho}</math>:<br>

			<math>\mathrm{F}_\mathrm{at}^\mathrm{amort}=c\dot{\rho}</math> , <math>\mathrm{F}_\mathrm{rep}^\mathrm{amort}=-c\dot{\rho}</math><br>

			In mechanical systems, dampers often appear in parallel with a spring. In that case, the force is formulated according to the criterion that has been chosen for the spring. When they are not part of a spring-damper group, the criterion is set arbitrarily.


			====✏️ Exemple D2.3: repulsive force of a damper with linear behaviour ====
			---------
			<small>
			[[File:EX D2-3-neut.png\|200px\|thumb\|left\|link=]]
			:La força de repulsió de l’amortidor s’obté a partir de l’allargament calculat a <span style="text-decoration: underline;"> [[D2. Forces d’interacció entre partícules#✏️ Exemple D2.2: força d’atracció d’una molla de comportament lineal\|'''l’exemple D2.2''']]</span> per derivació:<br>


			: <math>\rho=\sqrt{\mathrm{L}^2+(\mathrm{x}_1-\mathrm{x}_2)^2}\equiv \sqrt{\mathrm{L}^2+\mathrm{z}^2} \Rightarrow \dot{\rho}= \frac{\mathrm{d}\rho}{\mathrm{d}\mathrm{z}}\frac{\mathrm{d}\mathrm{z}}{\mathrm{d}\mathrm{t}}=\frac{\mathrm{z}\dot{\mathrm{z}}}{\sqrt{\mathrm{L}^2+\mathrm{z}^2}}</math><br>


			:<math>\mathrm{F}_\mathrm{rep}^\mathrm{amort}=-c \frac{\mathrm{z}\dot{\mathrm{z}}}{\sqrt{\mathrm{L}^2+\mathrm{z}^2}}=-c\frac{(\mathrm{x}_1-\mathrm{x}_2)(\dot{\mathrm{x}}_1-\dot{\mathrm{x}}_2)}{\sqrt{\mathrm{L}^2+\mathrm{(\mathrm{x}_1-\mathrm{x}_2})^2}}</math>
			</small>

	--------		--------