What is constraint equations: Definition and 13 Discussions

In computational chemistry, a constraint algorithm is a method for satisfying the Newtonian motion of a rigid body which consists of mass points. A restraint algorithm is used to ensure that the distance between mass points is maintained. The general steps involved are: (i) choose novel unconstrained coordinates (internal coordinates), (ii) introduce explicit constraint forces, (iii) minimize constraint forces implicitly by the technique of Lagrange multipliers or projection methods.
Constraint algorithms are often applied to molecular dynamics simulations. Although such simulations are sometimes performed using internal coordinates that automatically satisfy the bond-length, bond-angle and torsion-angle constraints, simulations may also be performed using explicit or implicit constraint forces for these three constraints. However, explicit constraint forces give rise to inefficiency; more computational power is required to get a trajectory of a given length. Therefore, internal coordinates and implicit-force constraint solvers are generally preferred.
Constraint algorithms achieve computational efficiency by neglecting motion along some degrees of freedom. For instance, in atomistic molecular dynamics, typically the length of covalent bonds to hydrogen are constrained; however, constraint algorithms should not be used if vibrations along these degrees of freedom are important for the phenomenon being studied.

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  1. M

    Engineering Kinematic modelling of a mechanism (General Crank)

    Hi, I was wondering if you could help me with a job at the university that consists of the kinematic modeling of mechanism number 3 in the image attached to this message. I have to set up the constraint equations and then solve the position, velocity and acceleration problem. For now I would...
  2. nish95

    About the constraint equations of a pulley

    See the solved example as shown in the image. I don't understand how can we write S(A)=2S(B) since integrating V(A)=2V(B) will give us an extra unknown constant and the work done by friction will depend on it. I found the relation 2S(B) + S(A) = const. (somebody confirm if this is right?) so...
  3. Kushal Chakrabarti

    Constraint equations in mechanics

    1. The problem: Two blocks of mass m=5kg and M= 10kg are connected by a string passing over a pulley B. Another string connects pulley B to the floor and passes over pulley A. An upward force F is applied at the centre of pulley A. Both pulleys are massless. Find acceleration of the blocks if F...
  4. Titan97

    Constraint Equations Homework: v0, v1, v2

    Homework Statement Block C is moving with a velocity v0 and block A and B are moving with velocities v1 and v2 with respect to block C. Find the relation between v0, v1 and v2 Homework Equations none The Attempt at a Solution Since the string is in-extensible, its velocity at both ends...
  5. J

    How Does Acceleration Relate Between Two Blocks in a Frictionless Pulley System?

    Homework Statement In the system shown, the strings and the pulleys are ideal. There is no friction anywhere in the system. As the system is released, block m1 moves downward. If the magnitude of the acceleration of block m1 is a, what is the magnitude of the acceleration of block m2?Homework...
  6. A

    How do constraint equations in mechanics work?

    How do constraint equations in mechanics work? Hi, friends! I'm having some trouble understanding the constraint equations:- (1) How do they relate the length of the string to the position of the block attached to it? The position of the block must be a vector and it must be differentiated...
  7. V

    Sliding bar constraint equations

    Homework Statement A uniform rod of length l rests on a horizontal floor and leans against a vertical wall, making an angle \theta with the floor. It is initially held at rest. At t = 0, the rod is released and falls, sliding on the floor and the wall with no friction. The only forces acting on...
  8. I

    Dynamics holonomic nonholonomic constraint equations

    Homework Statement Please see the attached file for the problem and figure. Homework Equations The Attempt at a Solution This is what I have so far: The position vector of the block, pblock= xblock wx+ yblock wy pblock dot omegaz=0 holonomic constraint equation (dot product) n=3N-M...
  9. G

    Constraint Equations for Particle on Rotating Ring

    Homework Statement A particle of mass M is constrained to move on a ring of radius r which rotates about a vertical axis (Y) passing through the center at a constant angular speed (omega). I am to find the constraint equation(s) for this system. The origin of the system is at the...
  10. S

    Constraint Equations: Atwoods Machine

    Can questions like the one given in the following pic be solved by taking the reference frame answhere in the middle of the string and not on the fixed pulley?(http://cnx.org/content/m14731/latest/pq8.gif) A somewhat similar method has been given in http://cnx.org/content/m14783/latest/"...
  11. B

    Einstein Vacuum Equation, Vacuum Constraint Equations

    Having a Lorentzian 4-manifold, the Einstein vacuum equations of general relativity read \overline R_{\alpha \beta} - \frac{1}{2}\overline g_{\alpha\beta}\overline R=0 where \overline R the scalar curvature, \overline g_{\alpha\beta} the metric tensor and \overline R_{\alpha\beta} the Ricci...
  12. S

    Solving constraint equations [Term Paper, HELP ]

    Solving constraint equations [Term Paper, HELP please] Hi, I am new here. I'm not sure if this fits in calculus&analysis forum, but i figured its not really simple math so, please move it into approprieate area if deemed necessary... I am doing materials selection analysis and my constraint...