How to simulate a full-suspension bike? As a fun project, I would like to roughly simulate the suspension operation of a full-suspension mountain bike. This is not another one of those "How does a bicycle stay upright?" questions.
Follow some metrics of interest.


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*Pedal bob - the amount of movement in the rear triangle upon pedaling up an incline. An estimate of the lost energy due to this.

*Sharp obstacle transient response - for example how does the bike move, when hitting a curb at high speed.

*Large obstacle transient response - for example, how does the bike move when it falls (along with the rider) 1 meter.


I am somewhat familiar with python, Mathematica, ScyLab, Matlab, Ansys. I guess an analytical solution would be too difficult.
Which approach will give quickly a parameterizable model and analyze it for the abovementioned information?
Here several common frame variations are mentioned.
EDIT:
More concretely:


*

*What model to use? Is there a widespread "bicycle" model for dynamic analysis?

*What software to utilize, in order to help me solve the problem?

 A: You need to start by writing down the equations of motion.  These can be obtained solely from energy considerations using the Lagrangian formulation of classical mechanics.  The suspension on the front fork should be relatively easy to account for, but the rear suspension could be more difficult since some of them have rather complicated geometries.  If you use the Lagrangian formalism, you will have to add the damping in the two suspensions manually afterwards, but again this isn't too difficult. 
Once you've obtained the equations of motion, the rest is just legwork.  You can convert these equations of motion to an equivalent state space model of a control system.  Matlab, Mathematica, and Python can all handle state space systems, but the most user-friendly and well developed is probably Matlab.  In addition, if you have access to the Simulink package together with your Matlab distribution, then you will be able to draw your simulation in picture format without having to figure out all of the underlying Matlab commands.  
The summary is: write down the equations of motion, convert them to a state space model, and import this to Matlab.  Come back with more specific questions if you get stuck along the way!
A: You need a good kinematic solver, to get the axle position path. At any point you can find by evaluating the instant center of rotation of the rear triangle. For 1) and 2) the center is fixed as there is single pivot. For 3) and 4) they indicate a virtual pivot, which is incorrectly placed. In reality it lies on the virtual intersection of the upper and lower bar, way to the left of the picture. In fact it looks like it should be close to the front wheel axle (which might be a good thing).
Then you must figure out the gearing ratio between the axle motion and the strut motion. This involves finding the instant center of motion of the activator bar which is typically fixed (except for 4 which I cannot figure out what is going on).
The two instant centers create two moment arms to the points of interest (axle and strut end) and the ratio of the moment arms gives the instant gearing ratio. This might be something like 2.5" of axle travel for each 1" of strut travel.
Once you have the kinematic model, then you need to estimate the spring-damper response to step inputs on the axle. If you want to include the all the degrees of freedom of the bike then you will end up with an extremely complicated model. This forum is not the place to explain it all out in details.
PS. 
All of these designs will exhibit linear stiffness and damping for small motion, and non-linear behavior for the full range of motion. The exact response does depend on the elasto-hydraulic properties of the strut element which are going to be very difficult to model without extensive testing. So some simplifications are in order.
