I am trying to find a study which addresses the loss of  power due to
inertia of pistons and connecting rods in a reciprocating internal
combustion engine.
The inertia is caused by the change in direction of the piston and
connecting rod at the ends of the stroke.

Hello and thank you for your question.

I have found the analysis you are looking for, at pages 22-27 of the
following Adobe Acrobat document (pages 2-2 to 2-9 in the original). 
The discussion is with respect to reciprocating compressors but the
dynamics of piston inertia and power costs is the same:
Gas Machinery Research Council Technical Report
http://www.gmrc.org/gmrc/pdf/!tr_97-2.pdf

Frankly, most of the mathematics in this paper is more than I can
handle, so I can only be of limited help to you in interpreting or
applying the analysis.

It appears that much of the budget for this sort of work emanates from
the energy industry.
Besides the Gas Machinery Research Council,
http://www.gmrc.org/gmrc/
There is other research material at the Gas Technology website at GTI
(The Gas Technology Institute).  For example, if you search for the
term "piston" at
http://www.gri.org/webroot/app/srch/srch.aspx
you will find the following material (summaries are available for free
but there are costs to ordering the full papers):
Ringless Piston Experiments
http://www.gri.org/webroot/app/xn/xd.aspx?xd=10AbstractPage\6062.xml
Advanced Automotive-Derivative Engine Development
http://www.gri.org/webroot/app/xn/xd.aspx?xd=10AbstractPage\10711.xml
Quantitive Diagnostics for Reciprocating Compressors.
http://www.gri.org/webroot/app/xn/xd.aspx?xd=10AbstractPage\3269.xml
Gas-Fueled Internal Combustion Engine Advancements: Task 1.1. Baseline
Literature Search
http://www.gri.org/webroot/app/xn/xd.aspx?xd=10AbstractPage\9935.xml

Google Search Terms Used:
"reciprocating engine" piston inertia
"reciprocating engine" quantify  piston inertia

Thanks again for allowing me to assist in answering your question.

If any of my answer is unclear to you, or if I can help you sort
through the material that is available, please let me know via a
'request for clarification of answer'.  I would appreciate it if you
would hold off on rating my answer until I have an opportunity to
respond.

Sincerely,
Google Answers Researcher
Richard-ga

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Request for Answer Clarification by derrell-ga on 06 Feb 2003 12:28 PST

Dear richard-ga:

Thanks for the work you have done to provide me with an answer to my
question.  I am disappointed that you were unable to find any
references to losses of power due to intertial forces in internal
combustion  engines but the information you provided on reciprocating
compressors and gas engines may be helpful.  We are evaluating it now.
 Perhaps I should have used the term "loss of efficiency (rather than
power) in reciprocating internal combustion gasoline engines due to
the inertia of pistons and connecting rods" because that is what we
are after.  Since compressors don't function from internal combustion
and gas engines probably have different characteristics from gasoline
engines, it is difficult to make comparisons.  Any further information
that you can provide would be appreciated. Perhaps the addition of
"internal combustion gasoline" to your search, if possible, would
help. This doesn't mean I am questioning or witholding the payment of
the fee.  Derrell

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Clarification of Answer by richard-ga on 06 Feb 2003 17:57 PST

Hello again:

After some experimentation the best search terms seem to be
piston inertia gasoline engine loss power
://www.google.com/search?hl=en&lr=&ie=UTF-8&oe=UTF-8&q=piston+inertia+gasoline+engine+loss+power

But again we're not finding the inertial forces for a gasoline-powered
up-and-down piston.

Is there anything useful to you in the discussion of the Ball Piston
Engine?
It's intended to be more efficient than the up-and-down piston
arrangement.
http://www.ballpistonengine.com/rep3.html
Perhaps these equations are meaningful to you?
http://www.ballpistonengine.com/rep2.html

Besides that, we're back to natural gas engines:
1999-01-2895 Preliminary Analysis of a Long Stroke Natural Gas ... 
http://www.eng.uts.edu.au/~samuel/sae1999.pdf

I think that's as much as we're going to find.

Sincerely,
richard-ga